Abstract:

This paper deals with the global asymptotic stability character of solutions of a discrete time deterministic model proposed by Wikan and Eide in Bulletin of Mathematical Biology, 66, 2004, 1685-1704. A stochastic extension of this model is proposed and discussed. Computer simulations suggest that the dynamics of the stochastic model includes a mixture of the dynamics observed in the deterministic model.

Paper's Title:

Stability of the D-Bar Reconstruction Method for Complex Conductivities

Author(s):

¹S. El Kontar, ¹T. El Arwadi, ¹H. Chrayteh, ²J.-M. Sac-Épée

¹Department of Mathematics and Computer Science,
Faculty of Science, Beirut Arab University,
P.O. Box: 11-5020, Beirut,
Lebanon.

E-mail: srs915@student.bau.edu.lb

²Institut Élie Cartan de Lorraine,
Université de Lorraine - Metz,
France.

Abstract:

In 2000, Francini solved the inverse conductivity problem for twice-differentiable conductivities and permittivities. This solution was considered to be the first approach using D-bar methods with complex conductivities. In 2012, based on Francini's work, Hamilton introduced a reconstruction method of the conductivity distribution with complex values. The method consists of six steps. A voltage potential is applied on the boundary. Solving a D-Bar equation gives the complex conductivity. In this paper, the stability of the D-Bar equation is studied via two approximations, t^exp and t^B, for the scattering transform. The study is based on rewriting the reconstruction method in terms of continuous operators. The conductivity is considered to be non smooth.

Paper's Title:

On a Generalized Biharmonic Equation in Plane Polars with Applications to Functionally Graded Materials

Author(s):

Ciro D'Apice

Department of Information Engineering and Applied Mathematics (DIIMA),
University of Salerno, 84084 Fisciano (SA),
Salerno, Italy.
dapice@diima.unisa.it

Abstract:

In this paper we consider a generalized biharmonic equation modelling a two-dimensional inhomogeneous elastic state in the curvilinear rectangle where denote plane polar coordinates. Such an arch--like region is maintained in equilibrium under self--equilibrated traction applied on the edge while the other three edges and are traction free. Our aim is to derive some explicit spatial exponential decay bounds for the specific Airy stress function and its derivatives. Two types of smoothly varying inhomogeneity are considered: (i) the elastic moduli vary smoothly with the polar angle, (ii) they vary smoothly with the polar distance. Such types of smoothly varying inhomogeneous elastic materials provide a model for technological important functionally graded materials. The results of the present paper prove how the spatial decay rate varies with the constitutive profile.

Paper's Title:

Viability Theory And Differential Lanchester Type Models For Combat.
Differential Systems.

Author(s):

G. Isac and A. Gosselin

Department Of Mathematics, Royal Military College Of Canada,
P.O. Box 17000, Stn Forces, Kingston, Ontario, Canada K7k 7b4
isac-g@rmc.ca
gosselin-a@rmc.ca
URL: http://www.rmc.ca/academic/math_cs/isac/index_e.html
URL: http://www.rmc.ca/academic/math_cs/gosselin/index_e.html

Abstract:

In 1914, F.W. Lanchester proposed several mathematical models based on differential equations to describe combat situations [34]. Since then, his work has been extensively modified to represent a variety of competitions including entire wars. Differential Lanchester type models have been studied from many angles by many authors in hundreds of papers and reports. Lanchester type models are used in the planning of optimal strategies, supply and tactics. In this paper, we will show how these models can be studied from a viability theory stand point. We will introduce the notion of winning cone and show that it is a viable cone for these models. In the last part of our paper we will use the viability theory of differential equations to study Lanchester type models from the optimal theory point of view.

Paper's Title:

MSplit Equality for Monotone Inclusion Problem and Fixed Point Problem in Real Banach Spaces

Author(s):

^1,2Christian Chibueze Okeke, ³Abdumalik Usman Bello, ¹Chinedu Izuchukwu, and ¹Oluwatosin Temitope Mewomo

¹School of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: okekec@ukzn.ac.za
E-mail: izuchukwuc@ukzn.ac.za
E-mail: mewomoo@ukzn.ac.za

²DST-NRF Center of Excellence in Mathematical and Statistical Sciences (CoE-Mass)
Johannesburg,
South Africa.

³Federal University,
Dutsin-Ma, Katsina State,
Nigeria.
E-mail: uabdulmalik@fudutsinma.edu.ng

Abstract:

In this paper a new iterative algorithm for approximating a common solution of split equality monotone inclusion problem and split equality fixed point problem is introduced. Using our algorithm, we state and prove a strong convergence theorem for approximating an element in the intersection of the set of solutions of a split equality monotone inclusion problem and the set of solutions of a split equality fixed point problem for right Bregman strongly nonexpansive mappings in the setting of p-uniformly convex Banach spaces which are also uniformly smooth. We also give some applications.

Paper's Title:

The Drazin-star and Star-Drazin Solutions to Quaternion Matrix Equations

Author(s):

Ivan I. Kyrchei, Dijana Mosić, Predrag Stanimirović

Pidstryhach Institute for Applied Problems of Mechanics and Mathematics
of NAS of Ukraine, L'viv, 79060,
Ukraine.
E-mail: ivankyrchei26@gmail.com

Faculty of Sciences and Mathematics, University of Niš, P.O.
Box 224, 18000, Niš, Serbia.
E-mail: dijana@pmf.ni.ac.rs

Faculty of Sciences and Mathematics, University of Niš, P.O.
Box 224, 18000, Niš, Serbia.
E-mail: pecko@pmf.ni.ac.rs

Abstract:

The notions of the Drazin-star and star-Drazin matrices are expanded to quaternion matrices in this paper. Their determinantal representations are developed in both cases in terms of noncommutative row-column determinants of quaternion matrices and for minors of appropriate complex matrices. We study all possible two-sided quaternion matrix equations with their one-sided partial cases whose uniquely determined solutions are based on the Drazin-star and star-Drazin matrices. Solutions of these equations are represented by Cramer's rules in both cases for quaternion and complex matrix equations. A numerical example is presented to illustrate our results.

Paper's Title:

Norm Estimates for the Difference between Bochner’s Integral and the Convex Combination of Function’s Values

Author(s):

P. Cerone, Y.J. Cho, S.S. Dragomir, J.K. Kim, and S.S. Kim

School of Computer Science and Mathematics,
Victoria University of Technology,
Po Box 14428, Mcmc 8001, Victoria, Australia.
pietro.cerone@vu.edu.au
URL: http://rgmia.vu.edu.au/cerone/index.html

Department of Mathematics Education, College of Education,
Gyeongsang National University, Chinju 660-701, Korea
yjcho@nongae.gsnu.ac.kr

School of Computer Science and Mathematics,
Victoria University of Technology,
Po Box 14428, Mcmc 8001, Victoria, Australia.
sever.dragomir@vu.edu.au
URL: http://rgmia.vu.edu.au/SSDragomirWeb.html

Department of Mathematics, Kyungnam University,
Masan,, Kyungnam 631-701, Korea
jongkyuk@kyungnam.ac.kr

Department of Mathematics, Dongeui University,
Pusan 614-714, Korea
sskim@dongeui.ac.kr

Abstract:

Norm estimates are developed between the Bochner integral of a vector-valued function in Banach spaces having the Radon-Nikodym property and the convex combination of function values taken on a division of the interval [a, b].

Paper's Title:

The Jacobson Density Theorem for Non-Commutative Ordered Banach Algebras

Author(s):

Kelvin Muzundu

University of Zambia,
Deparment of Mathematics and Statistics,
P.O. Box 32379, Lusaka,
Zambia.
E-mail: kmzundu@gmail.com

Abstract:

The Jacobson density theorem for general non-commutative Banach algebras states as follows: Let π be a continuous, irreducible representation of a non-commutative Banach algebra A on a Banach space X. If x₁,x₂,...,x_n are linearly independent in X and if y₁,y₂,...,y_n are in X, then there exists an a∈ A such that π(a)x_i=y_i for i=1,2,...,n. By considering ordered Banach algebras A and ordered Banach spaces X, we shall establish an order-theoretic version of the Jacobson density theorem.

Paper's Title:

Polynomial Dichotomy of C₀-Quasi Semigroups in Banach Spaces

Author(s):

Sutrima^1,2, Christiana Rini Indrati², Lina Aryati²

¹Department of Mathematics,
Universitas Sebelas Maret,
PO Box 57126, Surakarta,
Indonesia.
E-mail: sutrima@mipa.uns.ac.id

²Department of Mathematics,
Universitas Gadjah Mada,
PO Box 55281, Yogyakarta,
Indonesia.
E-mail: rinii@ugm.ac.id, lina@ugm.ac.id 

Abstract:

Stability of solutions of the problems is an important aspect for application purposes. Since its introduction by Datko [7], the concept of exponential stability has been developed in various types of stability by various approaches. The existing conditions use evolution operator, evolution semigroup, and quasi semigroup approach for the non-autonomous problems and a semigroup approach for the autonomous cases. However, the polynomial stability based on C₀-quasi semigroups has not been discussed in the references. In this paper we propose a new stability for C₀-quasi semigroups on Banach spaces i.e the polynomial stability and polynomial dichotomy. As the results, the sufficient and necessary conditions for the polynomial and uniform polynomial stability are established as well as the sufficiency for the polynomial dichotomy. The results are also confirmed by the examples.

Paper's Title:

A Self-adaptive Subgradient Extragradient Algorithm for Variational Inequality Problems and Fixed Point Problems in Banach Spaces

Author(s):

F. U. Ogbuisi

School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.

Department of Mathematics,
University of Nigeria, Nsukka,
Nigeria.
E-mail: ferdinard.ogbuisi@unn.edu.ng fudochukwu@yahoo.com

Abstract:

In this paper, we propose and analyze a type of subgradient extragradient algorithm for the approximation of a solution of variational inequality problem which is also a common fixed point of an infinite family of relatively nonexpansive mappings in 2-uniformly convex Banach spaces which are uniformly smooth. By using the generalized projection operator, we prove a strong convergence theorem which does not require the prior knowledge of the Lipschitz constant of cost operator. We further applied our result to constrained convex minimization problem, convex feasibility problem and infinite family of equilibrium problems. Our results improve and complement related results in 2-uniformly convex and uniformly smooth Banach spaces and Hilbert spaces.

Paper's Title:

Application of Equivalence Method to Classify Monge-Ampère Equations of Elliptic Type

Author(s):

Moheddine Imsatfia

E-mail: imsatfia@math.jussieu.fr 

Abstract:

In this paper, we apply Cartan's equivalence method to give a local classification of Monge-Ampère equations of elliptic type. Then we find a necessary and sufficient conditions such that a Monge-Ampère equation is either contactomorphic to the Laplace equation or to an Euler-Lagrange equation.

Paper's Title:

Operators On Frames

Author(s):

Javad Baradaran and Zahra Ghorbani

Department of Mathematics,
Jahrom University, P.B. 7413188941,
Jahrom,
Iran.
E-mail: baradaran@jahromu.ac.ir

Department of Mathematics,
Jahrom University, P.B. 7413188941,
Jahrom,
Iran.
E-mail: ghorbani@jahromu.ac.ir

Abstract:

In this paper, we first show the conditions under which an operator on a Hilbert space H can be represented as sum of two unitary operators. Then, it is concluded that a Riesz basis for a Hilbert space H can be written as a sum of two orthonormal bases. Finally, the study proves that if A is a normal maximal partial isometry on a Hilbert space H and if {e_k}^∞_k=1 is an orthonormal basis for H, then {Ae_k}^∞_k=1 is a 1-tight frame for H.

Paper's Title:

On the Fock Representation of the Central Extensions of the Heisenberg Algebra

Author(s):

L. Accardi and A. Boukas

Centro Vito Volterra, Università di Roma Tor Vergata,
via Columbia 2, 00133 Roma,
Italy
accardi@volterra.mat.uniroma2.it 
URL: http://volterra.mat.uniroma2.it

Department of Mathematics,
American College of Greece,
Aghia Paraskevi, Athens 15342,
Greece
andreasboukas@acg.edu

Abstract:

We examine the possibility of a direct Fock representation of the recently obtained non-trivial central extensions of the Heisenberg algebra, generated by elements and E satisfying the commutation relations ,  and , where a and are dual, h is self-adjoint, E is the non-zero self-adjoint central element and We define the exponential vectors associated with the Fock space, we compute their Leibniz function (inner product), we describe the action of a, and h on the exponential vectors and we compute the moment generating and characteristic functions of the classical random variable corresponding to the self-adjoint operator

Paper's Title:

A Multivalued Version of the Radon-Nikodym Theorem, via the Single-valued Gould Integral

Author(s):

Domenico Candeloro¹, Anca Croitoru², Alina Gavriluţ², Anna Rita Sambucini¹

¹Dept. of Mathematics and Computer Sciences,
University of Perugia,
1, Via Vanvitelli -- 06123, Perugia,
Italy.
E-mail:  domenico.candeloro@unipg.it, anna.sambucini@unipg.it

²Faculty of Mathematics,
Al. I. Cuza University,
700506 Iaşi,
Romania.
E-mail: croitoru@uaic.ro, gavrilut@uaic.ro

Abstract:

In this paper we consider a Gould type integral of real functions with respect to a compact and convex valued not necessarily additive measure. In particular we will introduce the concept of integrable multimeasure and, thanks to this notion, we will establish an exact Radon-Nikodym theorem relative to a fuzzy multisubmeasure which is new also in the finite dimensional case. Some results concerning the Gould integral are also obtained.

Paper's Title:

Extension of Factorization Theorems of Maurey to s-positively Homogeneous Operators

Author(s):

Abdelmoumen Tiaiba

Department of Physics,
University of M'sila,
Algeria.
E-mail: tiaiba05@yahoo.fr

Abstract:

In the present work, we prove that the class of s-positively homogeneous operators is a Banach space. As application, we give the generalization of some Maurey factorization theorems to T which is a s-positively homogeneous operator from X a Banach space into L_p. Where we establish necessary and sufficient conditions to proof that T factors through L_q. After this we give extend result of dual factorization theorem to same class of operators above.

Paper's Title:

Some Moduli and Inequalities Related to Birkhoff Orthogonality in Banach Spaces

Author(s):

Dandan Du and Yongjin Li

Department of Mathematics,
Sun Yat-sen University,
Guangzhou, 510275,
P.R. China.
E-mail: dudd5@mail2.sysu.edu.cn

 
Department of Mathematics,
Sun Yat-sen University,
Guangzhou, 510275,
P.R. China.
E-mail: stslyj@mail.sysu.edu.cn 

Abstract:

In this paper, we shall consider two new constants δ_B(X) and ρ_B(X), which are the modulus of convexity and the modulus of smoothness related to Birkhoff orthogonality, respectively. The connections between these two constants and other well-known constants are established by some equalities and inequalities. Meanwhile, we obtain two characterizations of Hilbert spaces in terms of these two constants, study the relationships between the constants δ_B(X), ρ_B(X) and the fixed point property for nonexpansive mappings. Furthermore, we also give a characterization of the Radon plane with affine regular hexagonal unit sphere.

Paper's Title:

A relation between nuclear cones and full nuclear cones

Author(s):

G. Isac and A. B. Nemeth

Department of Mathematics,
Royal Military College of Canada,
P. O. Box 17000 STN Forces Kingston, Ontario,
Canada K7K 7B4.
isac-g@rmc.ca

Faculty of Mathematics and Computer Science,
Babes-Bolyai University,
3400 Cluj-Napoca,
Romania.
nemab@math.ubbcluj.ro

Abstract:

The notion of nuclear cone in locally convex spaces corresponds to the notion of well based cone in normed spaces. Using the bipolar theorem from locally convex spaces it is proved that every closed nuclear cone is a full nuclear cone. Thus every closed nuclear cone can be associated to a mapping from a family of continuous seminorms in the space to the topological dual of the space. The relation with Pareto efficiency is discussed.

Paper's Title:

Approximation of an AQCQ-Functional Equation and its Applications

Author(s):

Choonkil Park and Jung Rye Lee

Department of Mathematics,
Research Institute for Natural Sciences,
Hanyang University, Seoul 133-791,
Korea;

Department of Mathematics,
Daejin University,
Kyeonggi 487-711,
Korea

baak@hanyang.ac.kr
jrlee@daejin.ac.kr

Abstract:

This paper is a survey on the generalized Hyers-Ulam stability of an AQCQ-functional equation in several spaces. Its content is divided into the following sections:

1. Introduction and preliminaries.

2. Generalized Hyers-Ulam stability of an AQCQ-functional equation in Banach spaces: direct method.

3. Generalized Hyers-Ulam stability of an AQCQ-functional equation in Banach spaces: fixed point method.

4. Generalized Hyers-Ulam stability of an AQCQ-functional equation in random Banach spaces: direct method.

5. Generalized Hyers-Ulam stability of an AQCQ-functional equation in random Banach spaces: fixed point method.

6. Generalized Hyers-Ulam stability of an AQCQ-functional equation in non-Archi-medean Banach spaces: direct method.

7. Generalized Hyers-Ulam stability of an AQCQ-functional equation in non-Archi-medean Banach spaces: fixed point method.

Paper's Title:

Strong Convergence Theorems for a Common Zero of an Infinite Family of Gamma-Inverse Strongly Monotone Maps with Applications

Author(s):

Charles Ejike Chidume, Ogonnaya Michael Romanus, and Ukamaka Victoria Nnyaba

African University of Science and Technology, Abuja,
Nigeria.
E-mail: cchidume@aust.edu.ng
E-mail: romanusogonnaya@gmail.com
E-mail: nnyabavictoriau@gmail.com

Abstract:

Let E be a uniformly convex and uniformly smooth real Banach space with dual space E^* and let A_k:E→E^*, k=1, 2, 3 , ...
be a family of inverse strongly monotone maps such that ∩^∞_k=1 A_k^-1(0)≠∅.
A new iterative algorithm is constructed and proved to converge strongly to a common zero of the family.
As a consequence of this result, a strong convergence theorem for approximating a common J-fixed point for an infinite family of
gamma-strictly J-pseudocontractive maps is proved. These results are new and improve recent results obtained for these classes of nonlinear maps.
Furthermore, the technique of proof is of independent interest.

Paper's Title:

On Perturbed Reflection Coefficients

Author(s):

J. L. Díaz-Barrero and J. J. Egozcue

Applied Mathematics III,
Universidad Politécnica de Cataluña,
Barcelona, Spain
jose.luis.diaz@upc.edu
juan.jose.egozcue@upc.edu

Abstract:

Many control and signal processing applications require testing stability of polynomials. Classical tests for locating zeros of polynomials are recursive, but they must be stopped whenever the so called "singular polynomials" appear. These ``singular cases'' are often avoided by perturbing the "singular polynomial". Perturbation techniques although always successful are not proven to be well-founded. Our aim is to give a mathematical foundation to a perturbation method in order to overcome "singular cases" when using Levinson recursion as a testing method. The non-singular polynomials are proven to be dense in the set of all polynomials respect the L²-norm on the unit circle . The proof is constructive and can be used algorithmically.

Paper's Title:

Solving Two Point Boundary Value Problems by Modified Sumudu Transform Homotopy Perturbation Method

Author(s):

Asem AL Nemrat and Zarita Zainuddin

School of Mathematical Sciences,
Universiti Sains Malaysia,
11800 Penang,
Malaysia.
E-mail: alnemrata@yahoo.com
zarita@usm.my

Abstract:

This paper considers a combined form of the Sumudu transform with the modified homotopy perturbation method (MHPM) to find approximate and analytical solutions for nonlinear two point boundary value problems. This method is called the modified Sumudu transform homotopy perturbation method (MSTHPM). The suggested technique avoids the round-off errors and finds the solution without any restrictive assumptions or discretization. We will introduce an appropriate initial approximation and furthermore, the residual error will be canceled in some points of the interval (RECP). Only a first order approximation of MSTHPM will be required, as compared to STHPM, which needs more iterations for the same cases of study. After comparing figures between approximate, MSTHPM, STHPM and numerical solutions, it is found through the solutions we have obtained that they are highly accurate, indicating that the MSTHPM is very effective, simple and can be used to solve other types of nonlinear boundary value problems (BVPs).

Paper's Title:

Global Analysis on Riemannian Manifolds

Author(s):

Louis Omenyi and Michael Uchenna

Department of Mathematics, Computer Science, Statistics and Informatics,
Alex Ekwueme Federal University, Ndufu-Alike,
Nigeria.
E-mail: omenyi.louis@funai.edu.ng, michael.uchenna@funai.edu.ng
URL: http://www.funai.edu.ng

Abstract:

In this paper, an exposition of the central concept of global analysis on a Riemannan manifold is given. We extend the theory of smooth vector fields from open subsets of Euclidean space to Riemannan manifolds. Specifically, we prove that a Riemannian manifold admits a unique solution for a system of ordinary differential equations generated by the flow of smooth tangent vectors. The idea of partial differential equations on Riemannian manifold is highlighted on the unit sphere.

Paper's Title:

A Unifying View of Some Banach Algebras

Author(s):

R. Kantrowitz

Mathematics & Statistics Department,
Hamilton College,
198 College Hill Road,
Clinton, NY 13323, USA.
E-mail: rkantrow@hamilton.edu

Abstract:

The purpose of this article is to shed light on a unifying framework for some normed algebras and, in particular, for some Banach algebras. The focus is on linear operators T between normed algebras X and Y and specified subalgebras A of Y. When the action of T on products in X satisfies a certain operative equation, the subspace T^-1(A) is stable under the multiplication of X and is readily equipped with a family of canonical submultiplicative norms. It turns out that many familiar and important spaces are encompassed under this versatile perspective, and we offer a sampling of several such. In this sense, the article presents an alternative lens through which to view a host of normed algebras. Moreover, recognition that a normed linear space conforms to this general structure provides another avenue to confirming that it is at once stable under multiplication and also outfitted with an abundance of equivalent submultiplicative norms.

Paper's Title:

Bartle Integration in Lie Algebras

Author(s):

Andreas Boukas and Philip Feinsilver

Centro Vito Volterra,
Universita di Roma Tor Vergata,
via Columbia 2, 00133 Roma,
Italy.

Department of Mathematics,
Southern Illinois University,
Carbondale, Illinois 62901,
USA.

E-mail: andreasboukas@yahoo.com
E-mail:  pfeinsil@math.siu.edu

Abstract:

Using Bartle's bilinear vector integral we define stochastic integrals of bounded operator valued functions with respect to Stieltjes measures associated with the generators of the Heisenberg and Finite Difference Lie algebras. Our definition also covers the Square of White Noise and sl/2 Lie algebras.

Paper's Title:

Strong Convergence Theorem for a Common Fixed Point of an Infinite Family of J-nonexpansive Maps with Applications

Author(s):

Charlse Ejike Chidume, Otubo Emmanuel Ezzaka and Chinedu Godwin Ezea

African University of Science and Technology,
Abuja,
Nigeria.
E-mail: cchidume@aust.edu.ng

Ebonyi State University,
Abakaliki,
Nigeria.
E-mail: mrzzaka@yahoo.com

 Nnamdi Azikiwe University,
Awka,
Nigeria.
E-mail: chinedu.ezea@gmail.com

Abstract:

Let E be a uniformly convex and uniformly smooth real Banach space with dual space E^*. Let {T_i}^∞_i=1 be a family of J-nonexpansive maps, where, for each i,~T_i maps E to 2^E*. A new class of maps, J-nonexpansive maps from E to E^*, an analogue of nonexpansive self maps of E, is introduced. Assuming that the set of common J-fixed points of {T_i}^∞_i=1 is nonempty, an iterative scheme is constructed and proved to converge strongly to a point x^* in ∩^∞_n=1F_JT_i. This result is then applied, in the case that E is a real Hilbert space to obtain a strong convergence theorem for approximation of a common fixed point for an infinite family of nonexpansive maps, assuming existences. The theorem obtained is compared with some important results in the literature. Finally, the technique of proof is also of independent interest.

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Paper's Title:

Shape Diagrams for 2D Compact Sets - Part III: Convexity Discrimination for Analytic and Discretized Simply Connected Sets.

Author(s):

S. Rivollier, J. Debayle and J.-C. Pinoli

Ecole Nationale Supérieure des Mines de Saint-Etienne,
CIS - LPMG, UMR CNRS 5148, 158 cours Fauriel,
42023 Saint-Etienne Cedex 2, France.

 rivollier@emse.fr; debayle@emse.fr; pinoli@emse.fr
 

Abstract:

Shape diagrams are representations in the Euclidean plane introduced to study 3-dimensional and 2-dimensional compact convex sets. However, they can also been applied to more general compact sets than compact convex sets. A compact set is represented by a point within a shape diagram whose coordinates are morphometrical functionals defined as normalized ratios of geometrical functionals. Classically, the geometrical functionals are the area, the perimeter, the radii of the inscribed and circumscribed circles, and the minimum and maximum Feret diameters. They allow twenty-two shape diagrams to be built. Starting from these six classical geometrical functionals, a detailed comparative study has been performed in order to analyze the representation relevance and discrimination power of these twenty-two shape diagrams. The two first parts of this study are published in previous papers 8,9. They focus on analytic compact convex sets and analytic simply connected compact sets, respectively. The purpose of this paper is to present the third part, by focusing on the convexity discrimination for analytic and discretized simply connected compact sets..

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Paper's Title:

Weakly Compact Composition Operators on Real Lipschitz Spaces of Complex-valued Functions on Compact Metric Spaces with Lipschitz Involutions

Author(s):

D. Alimohammadi and H. Alihoseini

Department of Mathematics,
Faculty of Science, Arak University
P. O. Box,38156-8-8349, Arak,
Iran.
E-mail: d-alimohammadi@araku.ac.ir
E-mail: hr_alihoseini@yahoo.com
URL: http://www.araku.ac.ir

Abstract:

We first show that a bounded linear operator T on a real Banach space E is weakly compact if and only if the complex linear operator T on the complex Banach space E_C is weakly compact, where E_C is a suitable complexification of E and iT' is the complex linear operator on E_C associated with T. Next we show that every weakly compact composition operator on real Lipschitz spaces of complex-valued functions on compact metric spaces with Lipschitz involutions is compact.

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Paper's Title:

Inequalities for Functions of Selfadjoint Operators on Hilbert Spaces:
a Survey of Recent Results

Author(s):

Sever S. Dragomir^1,2

¹Mathematics, College of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au

 
²DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL: https://rgmia.org/dragomir 

Abstract:

The main aim of this survey is to present recent results concerning inequalities for continuous functions of selfadjoint operators on complex Hilbert spaces. It is intended for use by both researchers in various fields of Linear Operator Theory and Mathematical Inequalities, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.

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Paper's Title:

On some Strongly Nonlinear Elliptic Problems in L¹-data with a Nonlinearity Having a Constant Sign in Orlicz Spaces via Penalization Methods

Author(s):

E. Azroul, A. Benkirane and M. Rhoudaf

Dep. Math., Faculté des Sciences Dhar-Mahraz,
B.P 1796 Atlas Fès,
Maroc

Departement of Mathematics,
Faculty of Sciences and Techniques of Tangier,
B.P. 416, Tangier,
Morocco.
rhoudaf_mohamed@yahoo.fr

Abstract:

This paper is concerned with the existence result of the unilateral problem associated to the equations of the type

in Orlicz spaces, without assuming the sign condition in the nonlinearity g. The source term f belongs to L¹(Ώ).

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Paper's Title:

A Study of the Effect of Density Dependence in a Matrix Population Model

Author(s):

N. Carter and M. Predescu

Department of Mathematical Sciences,
Bentley University,
Waltham, MA 02452,
U.S.A.
ncarter@bentley.edu
 mpredescu@bentley.edu

Abstract:

We study the behavior of solutions of a three dimensional discrete time nonlinear matrix population model. We prove results concerning the existence of equilibrium points, boundedness, permanence of solutions, and global stability in special cases of interest. Moreover, numerical simulations are used to compare the dynamics of two main forms of the density dependence function (rational and exponential).

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Paper's Title:

New Reverses of Schwarz, Triangle and Bessel Inequalities in Inner Product Spaces

Author(s):

S. S. Dragomir

School of Computer Science and Mathematics, Victoria University of Technology, PO BOX
14428, MCMC 8001, VICTORIA, AUSTRALIA.
sever.dragomir@vu.edu.au
URL: http://rgmia.vu.edu.au/SSDragomirWeb.html

Abstract:

New reverses of the Schwarz, triangle and Bessel inequalities in inner product spaces are pointed out. These results complement the recent ones obtained by the author in the earlier paper [13]. Further, they are employed to establish new Grüss type inequalities. Finally, some natural integral inequalities are stated as well.

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Paper's Title:

Simplicial (co)-homology of Band Semigroup

Author(s):

Yasser Farhat

Academic Support Department,
Abu Dhabi Polytechnic,
P.O. Box 111499, Abu Dhabi,
UAE.

E-mail: yasser.farhat@adpoly.ac.ae, farhat.yasser.1@gmail.com

Abstract:

We consider the Banach algebra l¹(S), with convolution, where S is a band semigroup. We prove directly, without using the cyclic cohomology, that the simplicial cohomology groups Hⁿ(l¹(S), l¹(S)^*) vanish for all n≥1. This proceeds in three steps. In each step, we introduce a bounded linear map. By iteration in each step, we achieve our goal.

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Paper's Title:

Some Notes on the Semi-open Subspaces of Topological Spaces

Author(s):

Nicky. K. Tumalun, Philotheus E. A. Tuerah, and Rolles N. S. Palilingan

Department of Mathematics
Universitas Negeri Manado
Tondano 95618
Indonesia.
E-mail: nickytumalun@unima.ac.id
URL: https://fmipa.unima.ac.id/

Department of Mathematics
Universitas Negeri Manado
Tondano 95618
Indonesia.
E-mail: pheatuerah@unima.ac.id
URL: https://fmipa.unima.ac.id/

Department of Physics
Universitas Negeri Manado
Tondano 95618
Indonesia.
E-mail: rollespalilingan@unima.ac.id
URL: https://fmipa.unima.ac.id/

Abstract:

In this paper, we obtain some new results regarding to the nowhere dense and first category set in the semi-open subspace of a topological space. More precisely, we prove that a nowhere dense set in the semi-open subspace of a topological space is equivalent as a nowhere dense set in that topological space. This implies that a first category set in the semi-open subspace of a topological space is equivalent as a first category set in that topological space. We also give some applications of these results to give some new proofs relating to the properties of semi-open set and Baire space.

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Paper's Title:

Positive Periodic Solutions for Second-Order Differential Equations with Generalized Neutral Operator

Author(s):

Wing-Sum Cheung, Jingli Ren and Weiwei Han

Department of Mathematics,
The University of Hong Kong
 Pokfulam Road,
Hong Kong

Department of Mathematics, Zhengzhou University
Zhengzhou 450001,
P.R. China
wscheung@hkucc.hku.hk
renjl@zzu.edu.cn

Abstract:

By some analysis of the neutral operator and an application of the fixed-point index theorem, we obtain sufficient conditions for the existence, multiplicity and nonexistence of periodic solutions to a second-order differential equation with the prescribed neutral operator, which improve and extend some recent results of Lu-Ge, Wu-Wang, and Zhang. An example is given to illustrate our results. Moreover, the analysis of the generalized neutral operator will be helpful for other types of differential equations.

 

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Paper's Title:

Generalizing Polyhedra to Infinite Dimension

Author(s):

Paolo d'Alessandro

Department of Mathematics, Third University of Rome,
Lgo S.L. Murialdo 1, 00146 Rome, Italy.

dalex@mat.uniroma3.it.

URL: http://www.mat.uniroma3.it/users/dalex/dalex.html.

Abstract:

This paper generalizes polyhedra to infinite dimensional Hilbert spaces as countable intersections of closed semispaces. Highlights are the structure theory that shows that a polyhedron is the sum of compact set (in a suitable topology) plus a closed pointed cone plus a closed subspace, giving the internal representation of polyhedra. In the final part the dual range space technique is extended to the solution of infinite dimensional LP problems.

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Paper's Title:

Weak solutions of non coercive stochastic Navier-Stokes equations in R²

Author(s):

Wilhelm Stannat and Satoshi Yokoyama

Technische Universität Berlin,
Strasse des 17. Juni 136, 10623 Berlin,
Germany.

Graduate School of Mathematical Sciences,
The University of Tokyo,
Komaba, Tokyo 153-8914,
Japan.

E-mail: stannat@math.tu-berlin.de

E-mail: satoshi2@ms.u-tokyo.ac.jp

Abstract:

We prove existence of weak solutions of stochastic Navier-Stokes equations in R² which do not satisfy the coercivity condition. The equations are formally derived from the critical point of some variational problem defined on the space of volume preserving diffeomorphisms in R². Since the domain of our equation is unbounded, it is more difficult to get tightness of approximating sequences of solutions in comparison with the case of a bounded domain. Our approach is based on uniform a priori estimates on the enstrophy of weak solutions of the stochastic 2D-Navier-Stokes equations with periodic boundary conditions, where the periodicity is growing to infinity combined with a suitable spatial cutoff-technique.

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Paper's Title:

On the Hyers-Ulam Stability of Homomorphisms and Lie Derivations

Author(s):

Javad Izadi and Bahmann Yousefi

Department of Mathematics, Payame Noor University,
P.O. Box: 19395-3697, Tehran,
Iran.
E-mail: javadie2003@yahoo.com, b_yousefi@pnu.ac.ir

 

Abstract:

Let A be a Lie Banach^*-algebra. For each elements (a, b) and (c, d) in A²:= A * A, by definitions

 (a, b) (c, d)= (ac, bd),
 |(a, b)|= |a|+ |b|,
(a, b)^*= (a^*, b^*),

A² can be considered as a Banach^*-algebra. This Banach^*-algebra is called a Lie Banach^*-algebra whenever it is equipped with the following definitions of Lie product:

for all a, b, c, d in A. Also, if A is a Lie Banach^*-algebra, then D: A²→A² satisfying

 D ([ (a, b), (c, d)])= [ D (a, b), (c, d)]+ [(a, b), D (c, d)]

for all $a, b, c, d∈A, is a Lie derivation on A². Furthermore, if A is a Lie Banach^*-algebra, then D is called a Lie^* derivation on A² whenever D is a Lie derivation with D (a, b)^*= D (a^*, b^*) for all a, b∈A. In this paper, we investigate the Hyers-Ulam stability of Lie Banach^*-algebra homomorphisms and Lie^* derivations on the Banach^*-algebra A².

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Paper's Title:

A Comparison Between Two Different Stochastic Epidemic Models with Respect to the Entropy

Author(s):

Farzad Fatehi and Tayebe Waezizadeh

Department of Mathematics,
University of Sussex,
Brighton BN1 9QH,
UK.
E-mail: f.fatehi@sussex.ac.uk
URL: http://www.sussex.ac.uk/profiles/361251

Department of Pure Mathematics, Faculty of Mathematics and Computer,
Shahid Bahonar University of Kerman,
Kerman 76169-14111,
Iran.
E-mail: waezizadeh@uk.ac.ir
URL: http://academicstaff.uk.ac.ir/en/tavaezizadeh

Abstract:

In this paper at first a brief history of mathematical models is presented with the aim to clarify the reliability of stochastic models over deterministic models. Next, the necessary background about random variables and stochastic processes, especially Markov chains and the entropy are introduced. After that, entropy of SIR stochastic models is computed and it is proven that an epidemic will disappear after a long time. Entropy of a stochastic mathematical model determines the average uncertainty about the outcome of that random experiment. At the end, we introduce a chain binomial epidemic model and compute its entropy, which is then compared with the DTMC SIR epidemic model to show which one is nearer to reality.

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Paper's Title:

Topological Aspects of Scalarization in Vector Optimization Problems.

Author(s):

Peter I. Kogut, Rosanna Manzo and Igor V. Nechay

Department of Differential Equations,
Dnipropetrovsk National University, Naukova STR.,
 13, 49010 Dnipropetrovsk,
Ukraine
 p.kogut@i.ua

Università di Salerno,
Dipartimento di Ingegneria dell'Informazione e Matematica Applicata,
Via Ponte don Melillo, 84084 Fisciano (SA),
Italy
 manzo@diima.unisa.it

Department of Technical Cybernetics,
Dnipropetrovsk Technical University,
Acad. Lazarjan STR., 2, 49010 Dnipropetrovsk,
Ukraine
 i.nechay@i.ua

Abstract:

In this paper, we study vector optimization problems in partially ordered Banach spaces. We suppose that the objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. We derive sufficient conditions for existence of efficient solutions of the above problems and discuss the role of topological properties of the objective space. We discuss the scalarization of vector optimization problems when the objective functions are vector-valued mappings with a weakened property of lower semicontinuity. We also prove the existence of the so-called generalized efficient solutions via the scalarization process. All principal notions and assertions are illustrated by numerous examples.

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Paper's Title:

Unital Compact Homomorphisms Between Extended Analytic Uniform Algebras

Author(s):

D. Alimohammadi and M. Mayghani

Department of Mathematics,
Faculty of Science, Arak University,
PO Box 38156-8-8349, Arak,
Iran.

d-alimohammadi@araku.ac.ir

m-maighany@yahoo.com

Abstract:

Let X and K be compact plane sets with K⊆X. We denote by A(X,K) and A(X) the algebras of all continuous complex-valued functions on X which are analytic on int(K) and int(X), respectively. It is known that A(X,K) and A(X) are natural uniform algebras on X. A(X) and A(X,K) are called analytic uniform algebra and extended analytic uniform algebra on X, respectively. In this paper we study unital homomorphisms between extended analytic uniform algebras and investigate necessary and sufficient conditions for which these homomorphisms to be compact. We also determine the spectrum of unital compact endomorphisms of extended analytic uniform algebras.

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Paper's Title:

Hyperbolic Models Arising in the Theory of Longitudinal Vibration of Elastic Bars

Author(s):

¹I. Fedotov, ¹J. Marais, ^1,2M. Shatalov and ¹H.M. Tenkam

¹Department of Mathematics and Statistics,
Tshwane University of Technology
 Private Bag X6680, Pretoria 0001
South Africa.

fedotovi@tut.ac.za, julian.marais@gmail.com, djouosseutenkamhm@tut.ac.za.

 ²Manufacturing and Materials
Council of Scientific and Industrial Research (CSIR)
P.O. Box 395, Pretoria, 0001
South Africa.
mshatlov@csir.co.za

 

Abstract:

In this paper a unified approach to the derivation of families of one
dimensional hyperbolic differential equations and boundary conditions describing
the longitudinal vibration of elastic bars is outlined. The longitudinal and
lateral displacements are expressed in the form of a power series expansion in
the lateral coordinate. Equations of motion and boundary conditions are derived
using Hamilton's variational principle. Most of the well known models in this
field fall within the frames of the proposed theory, including the classical
model, and the more elaborated models proposed by by Rayleigh, Love, Bishop,
Mindlin, Herrmann and McNiven. The exact solution is presented for the
Mindlin-Herrmann case in terms of Green functions. Finally, deductions regarding
the accuracy of the models are made by comparison with the exact
Pochhammer-Chree solution for an isotropic cylinder.

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Paper's Title:

Stability of an Almost Surjective epsilon-Isometry in The Dual of Real Banach Spaces

Author(s):

Minanur Rohman, Ratno Bagus Edy Wibowo, Marjono

Department of Mathematics, Faculty of Mathematics and Natural Sciences,
Brawijaya University,
Jl. Veteran Malang 65145,
Indonesia.
E-mail: miminanira@gmail.com

Department of Mathematics, Faculty of Mathematics and Natural Sciences,
Brawijaya University,
Jl. Veteran Malang 65145,
Indonesia.
E-mail: rbagus@ub.ac.id

Department of Mathematics, Faculty of Mathematics and Natural Sciences,
Brawijaya University,
Jl. Veteran Malang 65145,
Indonesia.
E-mail: marjono@ub.ac.id

Abstract:

In this paper, we study the stability of epsilon-isometry in the dual of real Banach spaces. We prove that the almost surjective epsilon-isometry mapping is stable in dual of each spaces. The proof uses Gâteaux differentiability space (GDS), weak-star exposed points, norm-attaining operator, and some studies about epsilon-isometry that have been done before.

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Paper's Title:

A Note on Schur's Lemma in Banach Function Spaces

Author(s):

R. E. Castillo, H. Rafeiro and E. M. Rojas

Universidad Nacional de Colombia,
Departamento de Matematicas, Bogota,
Colombia.
E-mail: recastillo@unal.edu.co
 
United Arab Emirates University,
Department of Mathematical Sciences, Al Ain,
United Arab Emirates.
E-mail: rafeiro@uaeu.ac.ae

Universidad Nacional de Colombia,
Departamento de Matematicas, Bogota,
Colombia.
E-mail: emrojass@unal.edu.co

Abstract:

In this small note, in a self contained presentation, we show the validity of Schur's type lemma in the framework of Banach function spaces.

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Paper's Title:

Strongly Nonlinear Variational Parabolic Problems in Weighted Sobolev Spaces

Author(s):

L. Aharouch, E. Azroul and M. Rhoudaf

Dép. Math. Faculté des Sciences Dhar-Mahraz
B.P 1796 Atlas Fés,
Maroc.
rhoudaf_mohamed@yahoo.fr 

Abstract:

In this paper , we study the existence of a weak solutions for the initial-boundary value problems of the strongly nonlinear degenerated parabolic equation,

∂u	+A(u)+g(x,t,u,∇ u)=f
∂t

where A is a Leray-lions operator acted from L^p(0,T,W₀^1,p(Ώ,w)) into its dual. g(x,t,u,∇ u) is a nonlinear term with critical growth condition with respect to ∇ u and no growth with respect to u. The source term f is assumed to belong to L^p'(0,T,W^-1,p'(Ώ,w^*)).

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Paper's Title:

On Convergence Theorems of an Implicit Iterative Process with Errors for a Finite Family of Asymptotically quasi I-nonexpansive Mappings

Author(s):

Farrukh Mukhamedov and Mansoor Saburov

Department of Computational & Theoretical Sciences,
Faculty of Sciences, International Islamic University Malaysia,
P.O. Box, 141, 25710, Kuantan,
Malaysia

farrukh_m@iiu.edu.my

msaburov@gmail.com

http://www.iium.edu.my

Abstract:

In this paper we prove the weak and strong convergence of the implicit iterative process with errors to a common fixed point of a finite family {T_j}^N_i=1 of asymptotically quasi I_j-nonexpansive mappings as well as a family of {Ij}^N_j=1 of asymptotically quasi nonexpansive mappings in the framework of Banach spaces. The obtained results improve and generalize the corresponding results in the existing literature.

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Paper's Title:

Some New Generalizations of Jensen's Inequality with Related Results and Applications

Author(s):

Steven G. From

Department of Mathematics
University of Nebraska at Omaha
Omaha, Nebraska 68182-0243.

E-mail: sfrom@unomaha.edu

Abstract:

In this paper, some new generalizations of Jensen's inequality are presented. In particular, upper and lower bounds for the Jensen gap are given and compared analytically and numerically to previously published bounds for both the discrete and continuous Jensen's inequality cases. The new bounds compare favorably to previously proposed bounds. A new method based on a series of locally linear interpolations is given and is the basis for most of the bounds given in this paper. The wide applicability of this method will be demonstrated. As by-products of this method, we shall obtain some new Hermite-Hadamard inequalities for functions which are 3-convex or 3-concave. The new method works to obtain bounds for the Jensen gap for non-convex functions as well, provided one or two derivatives of the nonlinear function are continuous. The mean residual life function of applied probability and reliability theory plays a prominent role in construction of bounds for the Jensen gap. We also present an exact integral representation for the Jensen gap in the continuous case. We briefly discuss some inequalities for other types of convexity, such as convexity in the geometric mean, and briefly discuss applications to reliability theory.

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Paper's Title:

Multivalent Harmonic Mappings Convoluted With a Multivalent Analytic Function

Author(s):

Om P. Ahuja and Özlem Güney

Kent State University, Department of Mathematical Sciences,
14111, Claridon-Troy Road, Burton, Ohio 44021,
U.S.A.
oahuja@kent.edu

University of Dicle, Department of Mathematics,
Faculty of Science and Art, 21280 Diyarbakir,
Turkey
ozlemg@dicle.edu.tr

Abstract:

The object of this paper is to study certain geometric properties of a family of multivalent harmonic mappings in the plane convoluted with a multivalent analytic function in the open unit disc.

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Paper's Title:

Some Properties of the Solution of a Second Order Elliptic Abstract Differential Equation

Author(s):

A. Aibeche and K. Laidoune

Mathematics Department, Faculty of Sciences, University Ferhat Abbas, Setif,
Route de Scipion, 19000, Setif,
Algeria
aibeche@univ-setif.dz

Abstract:

In this paper we study a class of non regular boundary value problems for elliptic differential-operator equation of second order with an operator in boundary conditions. We give conditions which guarantee the coerciveness of the solution of the considered problem, the completeness of system of root vectors in Banach-valued functions spaces and we establish the Abel basis property of this system in Hilbert spaces. Finally, we apply this abstract results to a partial differential equation in cylindrical domain.

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Paper's Title:

On the Regularization of Hammerstein's type Operator Equations

Author(s):

E. Prempeh, I. Owusu-Mensah and K. Piesie-Frimpong

Department of Mathematics,
KNUST, Kumasi-
Ghana.

Department of Science Education,
University of Education,
Winneba

Department of Mathematics,
Presbyterian University College, Abetifi,
Ghana

E-mail: isaacowusumensah@gmail.com

E-mail: eprempeh.cos@knust.edu.gh

E-mail: piesie74@yahoo.com

Abstract:

We have studied Regularization of Hammerstein's Type Operator Equations in general Banach Spaces. In this paper, the results have been employed to establish regularized solutions to Hammerstein's type operator equations in Hilbert spaces by looking at three cases of regularization.

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Paper's Title:

An Analytical Solution of Perturbed Fisher's Equation Using Homotopy Perturbation Method (HPM), Regular Perturbation Method (RPM) and Adomian Decomposition Method (ADM)

Author(s):

Moussa Bagayogo, Youssouf Minoungou, Youssouf Pare

Departement de Mathematique,
Universite Ouaga I Pr Joseph Ki-Zerbo,
Burkina Faso.
E-mail: moussabagayogo94@gmail.com, m.youl@yahoo.fr, pareyoussouf@yahoo.fr.

Abstract:

In this paper, Homotopy Perturbation Method (HPM), Regular Pertubation Method (RPM) and Adomian decomposition Method (ADM) are applied to Fisher equation. Then, the solution yielding the given initial conditions is gained. Finally, the solutions obtained by each method are compared

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Paper's Title:

Residual-Based A Posteriori Error Estimates For A Conforming Mixed Finite Element Discretization of the Monge-Ampere Equation

Author(s):

J. Adetola, K. W. Houedanou and B. Ahounou

Institut de Mathematiques et de Sciences Physiques (IMSP),
Universite d'Abomey-Calavi
E-mail:  adetolajamal58@yahoo.com

Departement de Mathematiques,
Faculte des Sciences et Techniques (FAST),
Universite d'Abomey-Calavi
E-mail: khouedanou@yahoo.fr

Departement de Mathematiques,
Faculte des Sciences et Techniques (FAST),
Universite d'Abomey-Calavi
E-mail: bahounou@yahoo.fr

 

Abstract:

In this paper we develop a new a posteriori error analysis for the Monge-Ampere equation approximated by conforming finite element method on isotropic meshes in R². The approach utilizes a slight variant of the mixed discretization proposed by Gerard Awanou and Hengguang Li in [4]. The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient.

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Paper's Title:

Semigroup of Linear Operator In Bicomplex Scalars

Author(s):

Stanzin Kunga, Amjad Ali and Aditi Sharma

Department of Mathematics,
University of Jammu,
Jammu And Kashmir,
India.
E-mail: stanzinkunga19@gmail.com

 
Department of Mathematics,
University of Jammu,
Jammu And Kashmir,
India.
E-mail:  amjadladakhi687@gmail.com

Department of Mathematics,
University of Jammu,
Jammu And Kashmir,
India.
E-mail: aditi.sharmaro@gmail.com

 

Abstract:

In this paper, we have studied the generators of C₀-semigroups of bicomplex linear operators on BC-Banach modules. This work is based on [5].

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Paper's Title:

A general theory of decision making

Author(s):

Frank Hansen

Department of Economics,
University of Copenhagen,
Studiestraede 6, DK-1455 Copenhagen K
Denmark Frank.Hansen@econ.ku.dk
URL: http://www.econ.ku.dk/okofh

Abstract:

We formulate a general theory of decision making based on a lattice of observable events, and we exhibit a large class of representations called the general model. Some of the representations are equivalent to the so called standard model in which observable events are modelled by an algebra of measurable subsets of a state space, while others are not compatible with such a description. We show that the general model collapses to the standard model, if and only if an additional axiom is satisfied. We argue that this axiom is not very natural and thus assert that the standard model may not be general enough to model all relevant phenomena in economics. Using the general model we are (as opposed to Schmeidler [16]) able to rationalize Ellsberg's paradox without the introduction of non-additive measures.

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Paper's Title:

Approximation of Derivatives in a Singularly Perturbed Second Order Ordinary Differential Equation with Discontinuous Terms Arising in Chemical Reactor Theory

Author(s):

R. Mythili Priyadharshini and N. Ramanujam

Department of Mathematics, Bharathidasan University,
Tiruchirappalli - 620 024, Tamilnadu, India.
matram2k3@yahoo.com
URL: http://www.bdu.ac.in/depa/science/ramanujam.htm

Abstract:

In this paper, a singularly perturbed second order ordinary differential equation with a discontinuous convection coefficient arising in chemical reactor theory is considered. A robust-layer-resolving numerical method is suggested. An ε-uniform global error estimate for the numerical solution and also to the numerical derivative are established. Numerical results are provided to illustrate the theoretical results.

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Paper's Title:

Optimization and Approximation for Polyhedra in Separable Hilbert Spaces

Author(s):

Paolo d'Alessandro

Department of Mathematics,
Third University of Rome,
Italy.

E-mail: pdalex45@gmail.com

Abstract:

This paper studies infinite dimensional polyhedra, covering the case in which range spaces of operators defining inequality systems are not closed. A rangespace method of linear programming is generalized to infinite dimensions and finite dimensional methods of approximation are introduced.

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Paper's Title:

Algorithms for Nonlinear Problems Involving Strictly Pseudocontractive Mappings

Author(s):

Mathew Olajiire Aibinu¹, Surendra Colin Thakur², Sibusiso Moyo³

¹Institute for Systems Science & KZN E-Skill CoLab,
Durban University of Technology,
Durban 4000,
South Africa.

¹DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS),
Johannesburg,
South Africa.
E-mail: moaibinu@yahoo.com mathewa@dut.ac.za

² KZN E-Skill CoLab,
Durban University of Technology,
Durban 4000,
South Africa.
E-mail:  thakur@dut.ac.za

³Institute for Systems Science & Office of the DVC Research, Innovation & Engagement Milena Court,
Durban University of Technology,
 Durban 4000,
South Africa.
E-mail: dvcrie@dut.ac.za

 

Abstract:

The puzzles in approximating a fixed point of nonlinear problems involving the class of strictly pseudocontractive mappings are conquered in this paper through viscosity implicit rules. Using generalized contraction mappings, a new viscosity iterative algorithm which is implicit in nature is proposed and analysed in Banach spaces for the class of strictly pseudocontractive mappings. The computations and analysis which are used in the proposed scheme are easy to follow and this gives rooms for a broad application of the scheme. It is obtained that the proposed iterative algorithm converges strongly to a fixed point of a μ-strictly pseudocontractive mapping which also solves a variational inequality problem. The result is also shown to hold for finite family of strictly pseudocontractive mappings. A numerical example is given to show the skillfulness of the proposed scheme and its implementation.

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Paper's Title:

Generalized Triangular and Symmetric Splitting Method for Steady State Probability Vector of Stochastic Matrices

Author(s):

B. Harika, D. Rajaiah, L. P. RajKumar, Malla Reddy Perati

Department of Mathematics,
Kakatiya University
E-mail: hbolledla@gmail.com

Department of Mathematics,
Kakatiya Institute of Technology and Science
E-mail: dr.mh@kitsw.ac.in

Department of Mathematics,
Kakatiya University
E-mail: ladalla@gmail.com

Department of Mathematics,
Kakatiya University
E-mail: mperati@yahoo.com

Abstract:

To find the steady state probability vector of homogenous linear system π Q=0 of stochastic rate matrix Q, generalized triangular and symmetric (GTS) splitting method is presented. Convergence analysis and choice of parameters are given when the regularized matrix A=Q^T+ε I of the regularized linear system Ax=b is positive definite. Analysis shows that the iterative solution of GTS method converges unconditionally to the unique solution of the regularized linear system. From the numerical results, it is clear that the solution of proposed method converges rapidly when compared to the existing methods.

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Paper's Title:

Automatic Continuity of Generalized Derivations in Certain *-Banach Algebras

Author(s):

M. Aboulekhlef, Y. Tidli and M. Belam

Laboratory of Applied Mathematics and Information and Communication Technology Polydisciplinary
Faculty of Khouribga University of Sultan Moulay Slimane
Morocco.
E-mail: aboulekhlef@gmail.com y.tidli@gmail.com m.belam@gmail.com

Abstract:

Consider the map φ of the Banach algebra Β in Β, if there exists a derivation δ of Β in Β so that for every  x, y ∈ Β , φ(xy) =φ(x)y+xδ(y) . φ is called a generalized derivation of Β. In [9], Bresar introduced the concept of generalized derivations. We prove several results about the automatic continuity of generalized derivations on certain Banach algebras.

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Paper's Title:

Locally Bicomplex Convex Module and Their Applications

Author(s):

Stanzin Kunga and Aditi Sharma

Department of Mathematics,
University of Jammu,
Jammu And Kashmir,
India.
E-mail: stanzinkunga19@gmail.com

Department of Mathematics,
University of Jammu,
Jammu And Kashmir,
India.
E-mail: aditi.sharmaro@gmail.com

Abstract:

Let X be a locally BC convex module and L(X) be the family of all continuous bicomplex linear operators on X. In this paper, we study some concepts of D-valued seminorms on locally BC convex module. Further, we study the bicomplex version of C_o and (C_o,1) semigroup. The work of this paper is inspired by the work in [2] and [6].

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Paper's Title:

Long Time Behavior for a Viscoelastic Problem with a Positive Definite Kernel

Author(s):

Nasser-eddine Tatar

King Fahd University of Petroleum and Mineral, Department of Mathematical Sciences,
Dhahran, 31261 Saudi Arabia
tatarn@kfupm.edu.sa

Abstract:

We study the asymptotic behavior of solutions for an integro-differential problem which arises in the theory of viscoelasticity. It is proved that solutions go to rest in an exponential manner under new assumptions on the relaxation function in the memory term. In particular, we consider a new family of kernels which are not necessarily decreasing.

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Paper's Title:

New Stochastic Calculus

Author(s):

Moawia Alghalith

Department of Economics,
University of the West Indies, St. Augustine,
Trinidad and Tobago.

E-mail: malghalith@gmail.com
 

Abstract:

We present new stochastic differential equations, that are more general and simpler than the existing Ito-based stochastic differential equations. As an example, we apply our approach to the investment (portfolio) model.

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Paper's Title:

Iterative Approximation of Zeros of Accretive Type Maps, with Applications

Author(s):

Charles Ejike Chidume, Chinedu Godwin Ezea, and Emmanuel Ezzaka Otubo

African University of Science and Technology, Abuja,
Nigeria.
E-mail: cchidume@aust.edu.ng
E-mail: chinedu.ezea@gmail.com
E-mail: mrzzaka@yahoo.com

Department of Mathematics,
Nnamdi Azikiwe University,
Awka,
Nigeria
E-mail: chinedu.ezea@gmail.com

Ebonyi State University,
Abakaliki,
Nigeria
E-mail: mrzzaka@yahoo.com

Abstract:

Let E be a reflexive real Banach space with uniformly Gâteaux differentiable norm. Let J:E→ E^* be the normalized duality map on E and let A:E^*→ E be a map such that AJ is an accretive and uniformly continuous map. Suppose that (AJ)^-1(0) in nonempty. Then, an iterative sequence is constructed and proved to converge strongly to some u^* in (AJ)^-1(0). Application of our theorem in the case that E is a real Hilbert space yields a sequence which converges strongly to a zero of A. Finally, non-trivial examples of maps A for which AJ is accretive are presented..

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Paper's Title:

Dynamical Analysis of HIV/AIDS Epidemic Model with Two Latent Stages, Vertical Transmission and Treatment

Author(s):

Nur Shofianah, Isnani Darti, Syaiful Anam

Mathematics Department,Faculty of Mathematics and Natural Sciences.
University of Brawijaya,
Jl. Veteran, Malang 65145,
Indonesia.
E-mail: nur_shofianah@ub.ac.id, isnanidarti@ub.ac.id, syaiful@ub.ac.id

Abstract:

We discuss about dynamical analysis of HIV/AIDS epidemic model with two latent stages, vertical transmission and treatment. In this model, the spreading of HIV occurs through both horizontal and vertical transmission. There is also treatment for individual who has been HIV infected. The latent stage is divided into slow and fast latent stage based on the immune condition which varies for each individual. Dynamical analysis result shows that the model has two equilibrium points: the disease-free equilibrium point and the endemic equilibrium point. The existence and global stability of equilibrium points depend on the basic reproduction number R₀. When R₀ <1, only the disease-free equilibrium point exists. If R₀ >1, there are two equilibrium points, which are the disease-free equilibrium point and the endemic equilibrium point. Based on the result of stability analysis, the disease-free equilibrium point is globally asymptotically stable if R₀ <1, while if R₀ > 1 and p=q, the endemic equilibrium point will be globally asymptotically stable. In the end, we show some numerical simulations to support the analytical result.

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Paper's Title:

Bounds on the Jensen Gap, and Implications for Mean-Concentrated Distributions

Author(s):

Xiang Gao, Meera Sitharam, Adrian E. Roitberg

Department of Chemistry, and Department of Computer & Information Science & Engineering,
University of Florida,
Gainesville, FL 32611,
USA.
E-mail: qasdfgtyuiop@gmail.com
URL: https://scholar.google.com/citations?user=t2nOdxQAAAAJ

Abstract:

This paper gives upper and lower bounds on the gap in Jensen's inequality, i.e., the difference between the expected value of a function of a random variable and the value of the function at the expected value of the random variable. The bounds depend only on growth properties of the function and specific moments of the random variable. The bounds are particularly useful for distributions that are concentrated around the mean, a commonly occurring scenario such as the average of i.i.d. samples and in statistical mechanics.

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31: Paper Source PDF document

Paper's Title:

Some criteria for Subspace-hypercyclicity of C₀-semigroups

Author(s):

Mansooreh Moosapoor

Department of Mathematics,
Farhangian University, Tehran,
Iran.
E-mail: m.mosapour@cfu.ac.ir
mosapor110@gmail.com
 

Abstract:

We research subspace-hypercyclic C₀-semigroups in this paper. We present various types of subspace-hypercyclicity criteria for C₀-semigroups. Some of them are stronger than the criteria introduced before. Also, we state that if a C₀-semigroup (T_t}_{t≥ 0} satisfies in any of them, then (T_t⊕T_t}_{t≥ 0} is subspace-hypercyclic.

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Paper's Title:

Solving Strongly Nonlinear Fractional Fredholm Integral-Differential Equations in Caputo's Sense Using the SBA Method

Author(s):

Germain Kabore¹, Bakari Abbo², Ousseni So³ and Blaise Some¹

¹Laboratoire d'Analyse Numerique, Informatique et de Biomathmathiques (L.N.I.BIO),
Universite Joseph Ki-Zerbo,
Burkina Faso.
E-mail: germainkabore982@gmail.com, blaisesomeouaga1@gmail.com

²University of N'Damena, Tchad.
E-mail: bakariabbo@yahoo.fr

³Laboratoire d'Analyse Numerique, Informatique et de Biomathemathiques (L.N.I.BIO),
Ecole Normale Superieure,
Burkina Faso.
E-mail: sousseni@yahoo.fr

Abstract:

The work addressed in this article consists in constructing the exact solutions, where they exist, of fractional Fredholm-type integro-differential equations in the sense of Caputo. Our results are obtained using the SBA method. The simplification of the approach, the analysis of its convergence, and the generalization of this method to these types of highly nonlinear equations constitute our scientific contribution.

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Paper's Title:

Stability of a Mixed Additive, Quadratic and Cubic Functional Equation In Quasi-Banach Spaces

Author(s):

A. Najati and F. Moradlou

Department of Mathematics, Faculty of Sciences,
University of Mohaghegh Ardabili, Ardabil,
Iran
a.nejati@yahoo.com

Faculty of Mathematical Sciences,
University of Tabriz, Tabriz,
Iran
moradlou@tabrizu.ac.ir
 

Abstract:

In this paper we establish the general solution of a mixed additive, quadratic and cubic functional equation and investigate the Hyers--Ulam--Rassias stability of this equation in quasi-Banach spaces. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297--300.

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Paper's Title:

Mass Transportation Approach For Parabolic P-Biharmonic Equations

Author(s):

A. Soglo, K. W. Houedanou, J. Adetola

Institut de Mathematiques et de Sciences Physiques (IMSP)
 Universite d'Abomey-Calavi,
Rep. of Benin
E-mail: ambroiso.soglo@gmail.com

Departement de Mathematiques
Faculte des Sciences et Techniques (FAST)
Universite d'Abomey-Calavi,
Rep. of Benin
E-mail: khouedanou@yahoo.fr

Universite Nationale des Sciences, Technologie, Ingenierie et Mathematiques (UNSTIM,
Abomey,
Rep. of Benin
E-mail: adetolajamal58@yahoo.com

Abstract:

In this paper, we propose a mass transportation method to solving a parabolic p-biharmonic equations, which generalized the Cahn-Hilliard (CH) equations in R^N, N∈N^*. By using a time-step optimal approximation in the appropriate Wasserstein space, we define an approximate weak solution which converges to the exact solution of the problem. We also show that the solution under certain conditions may be unique. Therefore, we study the asymptotic behavior of the solution of the parabolic p-biharmonic problem.

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Paper's Title:

On Interaction of Discontinuous Waves in a Gas with Dust Particles

Author(s):

J. Jena

Department of Mathematics, Netaji Subhas institute of technology,
Sector-3, Dwarka, New Delhi - 110 075,
India.
jjena67@rediffmail.com
jjena@nsit.ac.in

Abstract:

In this paper, the interaction of the strong shock with the weak discontinuity has been investigated for the system of partial differential equations describing one dimensional unsteady plane flow of an inviscid gas with large number of dust particles. The amplitudes of the reflected and transmitted waves after interaction of the weak discontinuity through a strong shock are evaluated by exploiting the results of general theory of wave interaction.

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Paper's Title:

Closedness and Skew Self-Adjointness of Nadir's Operator

Author(s):

Mostefa Nadir and Abdellatif Smati

Department of Mathematics,
University of Msila 28000,
ALGERIA.
E-mail: mostefanadir@yahoo.fr
E-mail: smatilotfi@gmail.com

Abstract:

In this paper, we present some sufficient conditions which ensure the compactness, the normality, the positivity, the closedness and the skew self-adjointness of the unbounded Nadir's operator on a Hilbert space. We get also when the measurement of its adjointness is null and other related results are also established.

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Paper's Title:

Some New Mappings Related to Weighted Mean Inequalities

Author(s):

Xiu-Fen Ma

College of Mathematical and Computer,
Chongqing Normal University Foreign Trade and Business College,
No.9 of Xuefu Road, Hechuan District 401520,
Chongqing City,
The People's Republic of China.
E-mail: maxiufen86@163.com

Abstract:

In this paper, we define four mappings related to weighted mean inequalities, investigate their properties, and obtain some new refinements of weighted mean inequalities.

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Paper's Title:

D-Iterative Method for Solving a Delay Differential Equation and a Two-Point Second-Order Boundary Value Problems in Banach Spaces

Author(s):

Francis Akutsah¹, Akindele Adebayo Mebawondu², Oluwatosin Babasola³, Paranjothi Pillay⁴ and Ojen Kumar Narain⁵

¹School of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: 216040405@stu.ukzn.ac.za, akutsah@gmail.com

²School of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa. 
DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS),
Johannesburg,
South Africa.
Mountain Top University,
Prayer City, Ogun State,
Nigeria.
E-mail: dele@aims.ac.za

³Department of Mathematical Sciences,
University of Bath,
Claverton Down,
Bath, BA2 7AY
UK.
E-mail: ob377@bath.ac.uk

⁴School of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: pillaypi@ukzn.ac.za

⁵School of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: naraino@ukzn.ac.za

Abstract:

The purpose of this paper is to re-establish the convergence, stability and data dependence results established by [2] and [3] by removing the strong assumptions imposed on the sequences which were used to obtain their results. In addition, we introduced a modified approach using the D-iterative method to solve a two-point second-order boundary value problem, and also obtain the solution of a delay differential equations using the obtained results in this paper. The results presented in this paper do not only extend and improve the results obtained in [2, 3], it further extends and improve some existing results in the literature.

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Paper's Title:

A New Step Size Rule in Noor's Method for Solving General Variational Inequalities

Author(s):

Abdellah Bnouhachem

School of Management Science and Engineering, Nanjing University,
Nanjing, 210093
P.R. China.
babedallah@yahoo.com

Abstract:

In this paper, we propose a new step size rule in Noor's method for solving general variational inequalities. Under suitable conditions, we prove that the new method is globally convergent. Preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method.

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Paper's Title:

Ulam Stability of Functional Equations

Author(s):

Stefan Czerwik and Krzysztof Król

Institute of Mathematics
 Silesian University of Technology
 Kaszubska 23, 44-100 Gliwice,
Poland
Stefan.Czerwik@polsl.pl
Krzysztof.Krol@polsl.pl

Abstract:

In this survey paper we present some of the main results on Ulam-Hyers-Rassias stability for important functional equations.

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Paper's Title:

Fixed Points and Stability of the Cauchy Functional Equation

Author(s):

Choonkil Park and Themistocles M. Rassias

Department of Mathematics, Hanyang University,
Seoul 133-791,
Republic of Korea

Department of Mathematics, National Technical University of Athens,
Zografou Campus, 15780 Athens,
Greece

baak@hanyang.ac.kr
trassias@math.ntua.gr

Abstract:

Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in Banach algebras and of derivations on Banach algebras for the Cauchy functional equation.

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Paper's Title:

Real Interpolation Methods and Quasilogarithmic Operators

Author(s):

Ming Fan

School of Industrial Technology and Management,
Dalarna University, 781 88 Borlänge, Sweden
 fmi@du.se
URL: http://users.du.se/~fmi

Abstract:

The purpose of this paper is to deal with nonlinear quasilogarithmic operators, which possesses the uniformly bounded commutator property on various interpolation spaces in the sense of Brudnyi-Krugljak associated with the quasi-power parameter spaces. The duality, and the domain and range spaces of these operators are under consideration. Some known inequalities for the Lebesgue integration spaces and the trace classes are carried over to the non-commutative symmetric spaces of measurable operators affiliated with a semi-finite von Neumann algebra.

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28: Paper Source PDF document

Paper's Title:

On the Constant in a Transference Inequality for the Vector-valued Fourier Transform

Author(s):

Dion Gijswijt and Jan van Neerven

Delft University of Technology,
Faculty EEMCS/DIAM,
 P.O. Box 5031,
2600 GA Delft,
The Netherlands.

URL: http://aw.twi.tudelft.nl/~neerven/
URL: http://homepage.tudelft.nl/64a8q/

E-mail: J.M.A.M.vanNeerven@TUDelft.nl
E-mail: D.C.Gijswijt@TUDelft.nl

Abstract:

The standard proof of the equivalence of Fourier type on R^d and on the torus T^d is usually stated in terms of an implicit constant, defined as the minimum of a sum of powers of sinc functions. In this note we compute this minimum explicitly.

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Paper's Title:

On Singular Numbers of Hankel Matrices of Markov Functions

Author(s):

Vasily A. Prokhorov

Department of Mathematics and Statistics,
University of South Alabama,
Mobile, Alabama 36688-0002,
USA.
E-mail: prokhoro@southalabama.edu
URL: http://www.southalabama.edu/mathstat/people/prokhorov.shtml

Abstract:

Let E ⊂ (01,1) be a compact set and let μ be a positive Borel measure with support supp μ=E. Let

In the case when E=[a,b]⊂ (-1,1) and μ satisfies the condition dμ/dx>0 a.e. on E, we investigate asymptotic behavior of singular numbers σ_kn,n of the Hankel matrix D_n, where k_n/n→θ∈[0,1] as n→∞. Moreover, we obtain asymptotics of the Kolmogorov, Gelfand and linear k-widths, k=k_n, of the unit ball A_n,2 of P_n∩L₂(Γ) in the space L₂(μ,E), where Γ={z:|z|=1} and P_n is the class of all polynomials of the degree at most n.

 

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Paper's Title:

Orthogonal Collocation on Finite Elements Using Quintic Hermite Basis

Author(s):

P. Singh, N. Parumasur and C. Bansilal

University of KwaZulu-Natal,
School of Mathematics Statistics and Computer Sciences,
Private Bag X54001,
Durban, 4000,
South Africa.
E-mail: singhprook@gmail.com
parumasurn1@ukzn.ac.za
christelle18@gmail.com

Abstract:

In this paper we consider the orthogonal collocation on finite elements (OCFE) method using quintic Hermite (second degree smooth) basis functions and use it to solve partial differential equations (PDEs). The method is particularly tailored to solve third order BVPS and PDEs and to handle their special solutions such as travelling waves and solitons, which typically is the case in the KdV equation. The use of quintic polynomials and collocation using Gauss points yields a stable high order superconvergent method. OCFE using quintic Hermite basis is optimal since it is computationally more efficient than collocation methods using (first degree smooth) piecewise-polynomials and more accurate than the (third degree smooth) B-splines basis. Various computational simulations are presented to demonstrate the computational efficiency and versatility of the OCFE method.

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Paper's Title:

Refinement Inequalities Among Symmetric Divergence Measures

Author(s):

Inder Jeet Taneja

Departamento de Matemática,
Universidade Federal de Santa Catarina, 88.040-900
Florianópolis, Sc, Brazil
taneja@mtm.ufsc.br
URL: http://www.mtm.ufsc.br/~taneja

Abstract:

There are three classical divergence measures in the literature on information theory and statistics, namely, Jeffryes-Kullback-Leiber’s J-divergence, Sibson-Burbea-Rao’s Jensen- Shannon divegernce and Taneja’s arithemtic - geometric mean divergence. These bear an interesting relationship among each other and are based on logarithmic expressions. The divergence measures like Hellinger discrimination, symmetric χ²−divergence, and triangular discrimination are not based on logarithmic expressions. These six divergence measures are symmetric with respect to probability distributions. In this paper some interesting inequalities among these symmetric divergence measures are studied. Refinements of these inequalities are also given. Some inequalities due to Dragomir et al. [6] are also improved.

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Paper's Title:

The ε-Small Ball Drop Property

Author(s):

C. Donnini and A. Martellotti

Dipartimento di Statistica e Matematica per la Ricerca Economica,
Università degli Studi di Napoli "Parthenope",
Via Medina, 80133 Napoli,
Italy
chiara.donnini@uniarthenope.it

{Dipartimento di Matematica e Informatica,
Università degli Studi di Perugia,
Via Pascoli - 06123 Perugia,
Italy.
amart@dipmat.unipg.it
URL: www.dipmat.unipg.it/~amart/

Abstract:

We continue the investigation on classes of small sets in a Banach space that give alternative formulations of the Drop Property. The small sets here considered are the set having the small ball property, and we show that for sets having non-empty intrinsic core and whose affine hull contains a closed affine space of infinite dimension the Drop Property can be equivalently formulated in terms of the small ball property.

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Paper's Title:

Hyers-Ulam-Rassias Stability of a Generalized Jensen Functional Equation

Author(s):

A. Charifi, B. Bouikhalene, E. Elqorachi and A. Redouani

Department of
Mathematics, Faculty of Sciences,
Ibn Tofail University,
Kenitra, Morocco
charifi2000@yahoo.fr bbouikhalene@yahoo.fr

Department of
Mathematics, Faculty of Sciences,
Ibn Zohr University,
Agadir, Morocco
elqorachi@hotmail.com Redouani-ahmed@yahoo.fr
 

Abstract:

In this paper we obtain the Hyers-Ulam-Rassias stability for the generalized Jensen's functional equation in abelian group (G,+). Furthermore we discuss the case where G is amenable and we give a note on the Hyers-Ulam-stability of the K-spherical (n × n)-matrix functional equation.

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Paper's Title:

The Superstability of the Pexider Type Trigonometric Functional Equation

Author(s):

Gwang Hui Kim and Young Whan Lee

Department of Mathematics, Kangnam
University Yongin, Gyeonggi, 446-702, Korea.
 ghkim@kangnam.ac.kr

Department of Computer and Information Security
Daejeon University, Daejeon 300-716, Korea.
ywlee@dju.ac.kr
 

Abstract:

The aim of this paper is to investigate the stability problem for
the Pexider type (hyperbolic) trigonometric functional equation
f(x+y)+f(x+σy)=λg(x)h(y) under the conditions :
|f(x+y)+f(x+σy)- λg(x)h(y)|≤φ(x),
φ(y), and min {φ(x), φ (y)}.

As a consequence, we have generalized the results of stability for
the cosine(d'Alembert), sine, and the Wilson functional equations by J.
Baker, P. Găvruta, R. Badora and R. Ger, Pl.~Kannappan, and G.
H. Kim

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Paper's Title:

Generalized k-distance-balanced Graphs

Author(s):

Amir Hosseini and Mehdi Alaeiyan

Department of mathematics, Karaj Branch,
Islamic Azad university, Karaj,
Iran.
E-mail: amir.hosseini@kiau.ac.ir, hosseini.sam.52@gmail.com

Department of Mathematics,
Iran University of Science and Technology, Tehran,
Iran.
E-mail: alaeiyan@iust.ac.ir

Abstract:

A nonempty graph Γ is called generalized k-distance-balanced, whenever every edge ab has the following property: the number of vertices closer to a than to b, k^, times of vertices closer to b than to a, or conversely, k∈ N .In this paper we determine some families of graphs that have this property, as well as to prove some other result regarding these graphs.

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Paper's Title:

A Method of the Study of the Cauchy Problem for~a~Singularly Perturbed Linear Inhomogeneous Differential Equation

Author(s):

E. E. Bukzhalev and A. V. Ovchinnikov

Faculty of Physics,
Moscow State University,
1 Leninskie Gory,
Moscow, 119991,
Russia
E-mail: bukzhalev@mail.ru

Russian Institute for Scientific and Technical Information of the Russian Academy of Sciences,
20 Usievicha St., Moscow, 125190,
Russia
E-mail: ovchinnikov@viniti.ru

Abstract:

We construct a sequence that converges to a solution of the Cauchy problem for a singularly perturbed linear inhomogeneous differential equation of an arbitrary order. This sequence is also an asymptotic sequence in the following sense: the deviation (in the norm of the space of continuous functions) of its nth element from the solution of the problem is proportional to the (n+1)th power of the parameter of perturbation. This sequence can be used for justification of asymptotics obtained by the method of boundary functions.

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Paper's Title:

Convergence Speed of Some Random Implicit-Kirk-type Iterations for Contractive-type Random Operators

Author(s):

H. Akewe, K.S. Eke

Department of Mathematics,
Covenant University, 
Canaanland, KM 10, Idiroko Road, P. M. B. 1023, Ota, Ogun State,
Nigeria.
E-mail: hudson.akewe@covenantuniversity.edu.ng, kanayo.eke@covenantuniversity.edu.ng

Abstract:

The main aim of this paper is to introduce a stochastic version of multistep type iterative scheme called a modified random implicit-Kirk multistep iterative scheme and prove strong convergence and stability results for a class of generalized contractive-type random operators. The rate of convergence of the random iterative schemes are also examined through an example. The results show that our new random implicit kirk multistep scheme perform better than other implicit iterative schemes in terms of convergence and thus have good potentials for further applications in equilibrium problems in computer science, physics and economics.

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Paper's Title:

Commutator For Singular Operators On Variable Exponent Sequence Spaces And Their Corresponding Ergodic Version

Author(s):

A.M. Alphonse and S.S.S. Anupindi

Department of Mathematics,
Birla Institute of Technology And Science- Pilani,
Hyderabad Campus, Jawahar Nagar, Kapra Mandal,
District.-Medchal-500 078, Telangana,
India.
E-mail: alphonse@hyderabad.bits-pilani.ac.in
p20180442@hyderabad.bits-pilani.ac.in
URL: https://www.bits-pilani.ac.in/hyderabad/a-michael-alphonse
https://www.bits-pilani.ac.in/research_scholars/sri-sakti-swarup-anupindi

Abstract:

In this paper, we prove strong type inequality for maximal commutator of singular operator on weighted lp spaces. Using these results we prove strong type inequality for the maximal commutator of singular operator on variable exponent sequence spaces. Using Calderon-Coifman-Weiss transference principle we prove strong type inequality for maximal ergodic commutator of singular operator on a probability space equipped with measure preserving transformation U.

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Paper's Title:

ℵ0 Algebra and its Novel Application in Edge Detection

Author(s):

G. E. Chatzarakis¹, S. Dickson², S. Padmasekaran², S. L. Panetsos¹, and J. Ravi³

¹Electrical and Electronic Engineering Educators,
School of Pedagogical and Technological Education (ASPETE),
Marousi 15122, Athens,
Greece.
E-mail: geaxatz@otenet.gr, spanetsos@aspete.gr

²Mathematics, Periyar University,
Periyar Palkalai Nagar, Salem, 636011, Tamilnadu,
India.
E-mail: dix.bern@gmail.com, padmasekarans@periyaruniversity.ac.in

³Department of Mathematics, Amity University,
Bengaluru, Karnataka,
India.
E-mail: jravistat@gmail.com
 

Abstract:

In this paper a new type of ℵ₀-algebra has been defined. With its help, the fuzzy cross subalgebra and the fuzzy η-relation on the ℵ₀-algebra are introduced and their respective properties are derived. Moreover, the fuzzy cross ℵ₀-ideal of the ℵ₀-algebra is defined with some theorems and intuitionistic fuzzy ℵ₀-ideals of the ℵ₀-algebra are introduced. This fuzzy algebra concept is applied in image processing to detect edges. This ℵ₀-algebra is a novelty in the field of research.

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Paper's Title:

Maximal Singular Operators On Variable Exponent Sequence Spaces and Their Corresponding Ergodic Version

Author(s):

Sri Sakti Swarup Anupindi and Michael A. Alphonse

Department of Mathematics, Birla Institute of Technology And Science- Pilani,
Hyderabad Campus, Jawahar Nagar, Kapra Mandal,
District.-Medchal-500 078 Telangana,
India.
E-mail: p20180442@hyderabad.bits-pilani.ac.in alphonse@hyderabad.bits-pilani.ac.in
URL: https://www.bits-pilani.ac.in/hyderabad/a-michael-alphonse
https://www.bits-pilani.ac.in/research_scholars/sri-sakti-swarup-anupindi

Abstract:

In this paper, we prove strong and weak type inequalities of singular operators on weighted l_w^p(Z)$. Using these results, we prove strong type and weak type inequalities of the maximal singular operator of Calderon-Zygmund type on variable exponent sequence spaces l^p(·)(Z). Using the Calderon-Coifman-Weiss transference principle, we prove strong type, weak type inequalities of the maximal ergodic singular operator on L_w^p(X,B,μ) spaces, where (X,B,μ) is a probability space equipped with measure preserving transformation U.

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Paper's Title:

General Oscillations for Some Third Order Differential Systems with Nonlinear Acceleration Term

Author(s):

Awar Simon Ukpera

Department of Mathematics,
Obafemi Awolowo University,
Ile-Ife,
Nigeria.
aukpera@oauife.edu.ng

 

Abstract:

We generate some general nonuniform hypotheses for third order differential systems of the form X''' +F(t,X'' )+BX'+CX = P(t), in which B and C are not necessarily constant matrices. Some results requiring sharp conditions on this system have recently been published by the author in [5]. This work however examines more closely crucial properties associated with the generalised nature of the nonlinear acceleration term F, which were largely overlooked in the earlier paper.

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Paper's Title:

On Stan Ulam and his Mathematics

Author(s):

Krzysztof Ciesielski and Themistocles M. Rassias

Mathematics Institute, Jagiellonian University,
Łjasiewicza 6, 30-348 Kraków,
Poland
Department of Mathematics. National Technical University of Athens,
Zografou Campus, 15780 Athens,
Greece
Krzysztof.Ciesielski@im.uj.edu.pl
trassias@math.ntua.gr

Abstract:

In this note we give a glimpse of the curriculum vitae of Stan Ulam, his personality and some of the mathematics he was involved in.

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Paper's Title:

Differentiability of Distance Functions in p-Normed Spaces

Author(s):

M. S. Moslehian, A. Niknam, S. Shadkam Torbati

Department of Pure Mathematics, Centre of Excellence in Analysis on Algebraic Structures (CEAAS),,
 Ferdowsi University of Mashhad,
P. O. Box 1159, Mashhad,
Iran

moslehian@ferdowsi.um.ac.ir
niknam@math.um.ac.ir
shadkam.s@wali.um.ac.ir

Abstract:

The farthest point mapping in a p-normed space X is studied in virtue of the Gateaux derivative and the Frechet derivative. Let M be a closed bounded subset of X having the uniformly p-Gateaux differentiable norm. Under certain conditions, it is shown that every maximizing sequence is convergent, moreover, if M is a uniquely remotal set then the farthest point mapping is continuous and so M is singleton. In addition, a Hahn--Banach type theorem in $p$-normed spaces is proved.

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Paper's Title:

Robust Error Analysis of Solutions to Nonlinear Volterra Integral Equation in L^p Spaces

Author(s):

Hamid Baghani, Javad Farokhi-Ostad and Omid Baghani

Department of Mathematics, Faculty of Mathematics,
University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan,
Iran.
E-mail: h.baghani@gmail.com

Department of Mathematics, Faculty of Basic Sciences,
Birjand University of Technology, Birjand,
Iran.
E-mail: j.farrokhi@birjandut.ac.ir

Department of Mathematics and Computer Sciences,
Hakim Sabzevari University, P.O. Box 397, Sabzevar,
Iran.
E-mail: o.baghani@gmail.com

Abstract:

In this paper, we propose a novel strategy for proving an important inequality for a contraction integral equations. The obtained inequality allows us to express our iterative algorithm using a "for loop" rather than a "while loop". The main tool used in this paper is the fixed point theorem in the Lebesgue space. Also, a numerical example shows the efficiency and the accuracy of the proposed scheme.

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Paper's Title:

Existence and Estimate of the Solution for the Approximate Stochastic Equation to the Viscous Barotropic Gas

Author(s):

R. Benseghir and A. Benchettah

LANOS Laboratory,
Badji Mokhtar University,
PO Box 12,
Annaba, Algeria.
E-mail: benseghirrym@ymail.com, abenchettah@hotmail.com

Abstract:

A stochastic equation of a viscous barotropic gas is considered. The application of Ito formula to a specific functional in an infinite dimensional space allows us to obtain an estimate which is useful to analyse the behavior of the solution. As it is difficult to exploit this estimate, we study an approximate problem. More precisely, we consider the equation of a barotropic viscous gas in Lagrangian coordinates and we add a diffusion of the density. An estimate of energy is obtained to analyse the behavior of the solution for this approximate problem and Galerkin method is used to prove the existence and uniqueness of the solution.

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26: Paper Source PDF document

Paper's Title:

Action of Differential Operators On Chirpsconstruct On L^∞

Author(s):

Taoufik El Bouayachi and Naji Yebari

Laboratoire de Mathematiques et applications,
Faculty of sciences and techniques, Tangier,
Morocco.
E-mail: figo407@gmail.com, yebarinaji@gmail.com

Abstract:

We will study in this work the action of differential operators on L∞ chirps and we will give a new definition of logarithmic chirp. Finally we will study the action of singular integral operators on chirps by wavelet characterization and Kernel method.

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26: Paper Source PDF document

Paper's Title:

Semivectorial Bilevel Optimization on Affine-Finsler-Metric Manifolds

Author(s):

Faik Mayah¹, Ali S Rasheed² and Naseif J. Al- Jawari³

¹Department of Physics,
College of Sciences,
University of Wasit,
Iraq.
E-mail: faik.mayah@gmail.com

²Ministry of Higher Education and Scientific Research,
Iraq.
E-mail: ali.math2018@yahoo.com ahmedhashem@gmail.com

³Dept. of Mathematics,
College of Science,
Mustansiriyah University, Baghdad,
Iraq.
E-mail: nsaif642014@yahoo.com

Abstract:

A Finsler manifold is a differential manifold together with a Finsler metric, in this paper we construct a new class of Finsler metric affine manifolds on bilevel semivectorial with optimization problems. The first steps for this purpose involve the study of bilevel optimization on affine manifolds. The bilevel programming problem can be viewed as a static version of the noncooperative, two-person game which was introduced in the context of unbalanced economic markets. Bilevel optimization is a special kind of optimization where one problem is embedded within another.

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Paper's Title:

The Automatic Continuity of N-Homomorphisms in Certain *-Banach Algebras

Author(s):

M. Aboulekhlef, Y. Tidli

Laboratory of Applied Mathematics and Information and Communication Technology
Polydisciplinary Faculty of Khouribga
University of Sultan Moulay Slimane
Morocco.
E-mail: aboulekhlef@gmail.com y.tidli@gmail.com

Abstract:

In this study, we prove the automatic continuity of surjective n-homomorphism between complete p-normed algebras. We show also that if Α and Β are complete *-p-normed algebras, Β is *simple and ψ: Α → Β is a surjective n-homomorphism under certain conditions, then ψ is continuous.

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Paper's Title:

An Algorithm to Compute Gaussian-Type Quadrature Formulae
that Integrate Polynomials and Some Spline Functions Exactly

Author(s):

Allal Guessab

Laboratoire de Mathématiques Appliquées,
Université de Pau, 64000, Pau,
France.
allal.guessab@univ-pau.fr
URL: http://www.univ-pau.fr/~aguessab/

Abstract:

It is well-known that for sufficiently smooth integrands on an interval, numerical integration can be performed stably and efficiently via the classical (polynomial) Gauss quadrature formulae. However, for many other sets of integrands these quadrature formulae do not perform well. A very natural way of avoiding this problem is to include a wide class among arbitrary functions (not necessary polynomials) to be integrated exactly. The spline functions are natural candidates for such problems. In this paper, after studying Gaussian type quadrature formulae which are exact for spline functions and which contain boundary terms involving derivatives at both end points, we present a fast algorithm for computing their nodes and weights. It is also shown, taking advantage of the close connection with ordinary Gauss quadrature formula, that the latter are computed, via eigenvalues and eigenvectors of real symmetric tridiagonal matrices. Hence a new class of quadrature formulae can then be computed directly by standard software for ordinary Gauss quadrature formula. Comparative results with classical Gauss quadrature formulae are given to illustrate the numerical performance of the approach.

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Paper's Title:

Fixed Point Theorems for a Finite Family of Asymptotically Nonexpansive Mappings

Author(s):

E. Prempeh

Department of Mathematics,
Kwame Nkrumah University of Science and Technology,
Kumasi, Ghana
edward_prempeh2000@yahoo.com

Abstract:

Let be a real reflexive Banach space with a uniformly Gâteaux differentiable norm, be a nonempty bounded closed convex subset of i=1,2,...,r be a finite family of asymptotically nonexpansive mappings such that for each Let be a nonempty set of common fixed points of and define

. Let be fixed and let be such that as . We can prove that the sequence satisfying the relation

associated with , converges strongly to a fixed point of provided possesses uniform normal structure. Furthermore we prove that the iterative process:

, converges strongly to a fixed point of

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25: Paper Source PDF document

Paper's Title:

On the Optimal Buckling Loads of Clamped Columns

Author(s):

Samir Karaa

Department of Mathematics and Statistics
Sultan Qaboos University, P.O. Box 36, Alkhod 123
Muscat, Sultanate of Oman
skaraa@squ.edu.om

URL: http://ajmaa.org/EditorsU/SKaraa.php

Abstract:

We consider the problem of determining the optimal shape of a clamped column of given length and volume, without minimum cross section constraints. We prove that the necessary condition of optimality derived by Olhoff and Rasmussen is sufficient when 0<α<1. The number alpha appears in Equation 2.1. For the case α =1 it is shown that the value 48 is optimal. We also determine the exact values of the optimal shape at the extremities, and take advantage of a robust nonlinear ordinary differential equation solver COLSYS to compute the optimal buckling load with a high accuracy.

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Paper's Title:

Generalized Efficient Solutions to One Class of Vector Optimization Problems in Banach Space

Author(s):

Peter I. Kogut, Rosanna Manzo, and Igor V. Nechay

Department of Differential Equations,
Dnipropetrovsk National University,
Naukova str., 13, 49050 Dnipropetrovsk,
Ukraine
 p.kogut@i.ua

 Dipartimento di Ingegneria Dell’informazione e Matematica Applicata,
Università di Salerno,
Via Ponte Don Melillo, 84084 Fisciano (Sa),
Italy
manzo@diima.unisa.it

 Department of Technical Cybernetics,
Dnipropetrovsk Technical University,
Acad. Lazarjan str., 2, 49010
Dnipropetrovsk,
Ukraine
 i.nechay@i.ua

Abstract:

In this paper, we study vector optimization problems in Banach spaces for essentially nonlinear operator equations with additional control and state constraints. We assume that an objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. Using the penalization approach we derive both sufficient and necessary conditions for the existence of efficient solutions of the above problems. We also prove the existence of the so-called generalized efficient solutions via the scalarization of some penalized vector optimization problem.

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Paper's Title:

Common Fixed Point Results for Banach Operator Pairs and Applications to Best Approximation

Author(s):

Hemant Kumar Nashine

Department of Mathematics,
Disha Institute of Management and Technology,
Satya Vihar, Vidhansabha - Chandrakhuri Marg (Baloda Bazar Road), Mandir Hasaud,
Raipur - 492101(Chhattisgarh), India.

hemantnashine@rediffmail.com
nashine_09@rediffmail.com
 

Abstract:

The common fixed point results for Banach operator pair with generalized nonexpansive mappings in q-normed space have been obtained in the present work. As application, some more general best approximation results have also been determined without the assumption of linearity or affinity of mappings. These results unify and generalize various existing known results with the aid of more general class of noncommuting mappings.

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Paper's Title:

On Interpolation of L² functions

Author(s):

Anis Rezgui

Department of Mathematics,
Faculty of Sciences,
Taibah University, Al Madina Al Munawara,
KSA.

Mathematics Department,
INSAT,
University of Carthage, Tunis,
Tunisia
E-mail: anis.rezguii@gmail.com

Abstract:

In this paper we are interested in polynomial interpolation of irregular functions namely those elements of L²(R,μ) for μ a given probability measure. This is of course doesn't make any sense unless for L² functions that, at least, admit a continuous version. To characterize those functions we have, first, constructed, in an abstract fashion, a chain of Sobolev like subspaces of a given Hilbert space H₀. Then we have proved that the chain of Sobolev like subspaces controls the existence of a continuous version for L² functions and gives a pointwise polynomial approximation with a quite accurate error estimation.

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Paper's Title:

The Dynamics of an Ebola Epidemic Model with Quarantine of Infectives

Author(s):

Eliab Horub Kweyunga

Department of Mathematics,
Kabale University,
P.O.Box 317, Kabale,
Uganda.

E-mail: hkweyunga@kab.ac.ug

Abstract:

The recurrent outbreaks of ebola in Africa present global health challenges. Ebola is a severe, very fatal disease with case fatality rates of up to 90%. In this paper, a theoretical deterministic model for ebola epidemic with quarantine of infectives is proposed and analyzed. The model exhibits two equilibria; the disease free and endemic equilibrium points. The basic reproduction number, R₀, which is the main threshold, is obtained and the stability of the equilibrium points established. Using parameter values drawn from the 2014 West Africa ebola outbreak, a numerical simulation of the model is carried out. It is found that the dynamics of the model are completely determined by R₀ and that a quarantine success rate of at least 70% is sufficient to contain the disease outbreak.

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Paper's Title:

Numerical Radius Isometries between Hermitian Banach Algebras

Author(s):

Mohamed Mabrouk and Ashwaq Albideewi

Department of Mathematics,
Faculty of Sciences Cite Erriadh,
University of Gabes,
6072 Zrig, Gabes,
Tunisia.
E-mail: mohamed.mabrouk@fsg.rnu.tn

 Department of Mathematics,
College of Applied Sciences,
Umm Al-Qura University,
P. O. Box 715,
Makkah 21955,
Saudi Arabia.
Email: Ashwaq.F.B@hotmail.com

Abstract:

In the case of C*-algebras, the author in [2] showed that any linear unital and surjective numerical radius isometry is a Jordan *-isomorphism. In this paper, we generalize this result to the case of Hermitian Banach algebras.

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Paper's Title:

Generalized Von Neumann-Jordan Constant for Morrey Spaces and Small Morrey Spaces

Author(s):

H. Rahman and H. Gunawan

Department of Mathematics,
Islamic State University Maulana Malik Ibrahim Malang,
Jalan Gajayana No.50,
Indonesia.
E-mail: hairur@mat.uin-malang.ac.id

Analysis and Geometry Group,
Faculty of Mathematics and Natural Sciences,
Bandung Institute of Technology, Bandung 40132,
Indonesia.
E-mail: hgunawan@math.itb.ac.id
URL:  http://personal.fmipa.itb.ac.id/hgunawan/

Abstract:

In this paper we calculate some geometric constants for Morrey spaces and small Morrey spaces, namely generalized Von Neumann-Jordan constant, modified Von Neumann-Jordan constants, and Zbaganu constant. All these constants measure the uniformly nonsquareness of the spaces. We obtain that their values are the same as the value of Von Neumann-Jordan constant for Morrey spaces and small Morrey spaces.

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Paper's Title:

Walrasian Equilibrium for Set-valued Mapping

Author(s):

M. Muslikh, R.B.E Wibowo, S. Fitri

Department of Mathematics,
University of Brawijaya,
Malang,
Indonesia.
E-mail: mslk@ub.ac.id
rbagus@ub.ac.id
saadatul@ub.ac.id

Abstract:

In this article, we obtain the existence of Walras equilibrium for set-valued demand mappings in a pure exchange economy. In this case, the set-valued mappings are defined by the loss function. Therefore, we shall summarize the features describing the exchange economy system which contain the loss function.

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Paper's Title:

Credibility Based Fuzzy Entropy Measure

Author(s):

G. Yari, M. Rahimi, B. Moomivand and P. Kumar

Department of Mathematics,
Iran University of Science and Technology,
Tehran,
Iran.
E-mail: Yari@iust.ac.ir
E-mail: Mt_Rahimi@iust.ac.ir
URL: http://www.iust.ac.ir/find.php?item=30.11101.20484.en
URL: http://webpages.iust.ac.ir/mt_rahimi/en.html

Qarzol-hasaneh
Mehr Iran Bank, Tehran,
Iran.
E-mail: B.moomivand@qmb.ir

Department of Mathematics and Statistics,
University of Northern British Columbia,
Prince George, BC,
Canada.
E-mail: Pranesh.Kumar@unbc.ca

Abstract:

Fuzzy entropy is the entropy of a fuzzy variable, loosely representing the information of uncertainty. This paper, first examines both previous membership and credibility based entropy measures in fuzzy environment, and then suggests an extended credibility based measure which satisfies mostly in Du Luca and Termini axioms. Furthermore, using credibility and the proposed measure, the relative entropy is defined to measure uncertainty between fuzzy numbers. Finally we provide some properties of this Credibility based fuzzy entropy measure and to clarify, give some examples.

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Paper's Title:

Some Convergence Results for  Jungck-Am Iterative Process In Hyperbolic Spaces

Author(s):

Akindele Adebayo Mebawondu and Oluwatosin Temitope Mewomo

School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: 216028272@stu.ukzn.ac.za, mewomoo@ukzn.ac.za

Abstract:

In this paper, we introduce a new three steps iterative process called Jungck-AM iterative process and show that the proposed iterative process can be used to approximate fixed points of Jungck-contractive type mappings and Jungck-Suzuki type mappings. In addition, we establish some strong and Δ-convergence results for the approximation of fixed points of Jungck-Suzuki type mappings in the frame work of uniformly convex hyperbolic space. Furthermore, we show that the newly proposed iterative process has a better rate of convergence compare to the Jungck-Noor, Jungck-SP, Jungck-CR and some existing iterative processes in the literature. Finally, stability, data dependency results for Jungck-AM iterative process is established and we present an analytical proof and numerical examples to validate our claim.

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Paper's Title:

Construction of a Frame Multiresolution Analysis on Locally Compact Abelian Groups

Author(s):

R. Kumar and Satyapriya

Department of Mathematics,
Kirori Mal College,
University of Delhi,
Delhi,
India.
E-mail: rajkmc@gmail.com

 
Department of Mathematics,
University of Delhi,
Delhi,
India.
E-mail: kmc.satyapriya@gmail.com

Abstract:

The frame multiresolution analysis (FMRA) on locally compact Abelian groups has been studied and the results concerning classical MRA have been worked upon to obtain new results. All the necessary conditions, which need to be imposed on the scaling function φ to construct a wavelet frame via FMRA, have been summed up. This process of construction of FMRA has aptly been illustrated by sufficient examples.

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Paper's Title:

Derivation of the Existence Theorem of the Solution of the Stochastic Functional Differential Equation Using Conditions Given Partial Weights

Author(s):

Young-Ho Kim

Department of Mathematics,
Changwon National University
Changwon, Gyeongsangnam 51140,
Korea.
E-mail: yhkim@changwon.ac.kr

Abstract:

The main purpose of this note was to demonstrate the solution existence theorem for stochastic functional differential equations under sufficient conditions. As an alternative to the stochastic process theory of the stochastic functional differential equations, we impose a partial weighting condition and a weakened linear growth condition. We first show that the condition guarantees existence and uniqueness and then show some exponential estimates for the solution.

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Paper's Title:

Comparison Results for Solutions of Time Scale Matrix Riccati Equations and Inequalities

Author(s):

R. Hilscher

Department of Mathematical Analysis, Faculty of Science,
Masaryk University, Janáčkovo nám. 2a,
CZ-60200, Brno, Czech Republic.
hilscher@math.muni.cz
URL: http://www.math.muni.cz/~hilscher/

Abstract:

In this paper we derive comparison results for Hermitian solutions of time scale matrix Riccati equations and Riccati inequalities. Such solutions arise from special conjoined bases (X,U) of the corresponding time scale symplectic system via the Riccati quotient . We also discuss properties of a unitary matrix solution of a certain associated Riccati equation.

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Paper's Title:

Existence of solutions for Neutral Stochastic Functional Differential Systems with Infinite Delay in Abstract Space

Author(s):

P. Balasubramaniam, A. V. A. Kumar and S. K. Ntouyas

Department of Mathematics, Gandhigram Rural Institute,
Deemed University, Gandhigram - 624 302, Tamil Nadu, India.
pbalgri@rediffmail.com

Department of Mathematics, Gandhigram Rural Institute,
Deemed University, Gandhigram - 624 302, Tamil Nadu, India.
nnddww@tom.com

Department of Mathematics, University of Ioannina,
451 10 Ioannina,
Greece.
sntouyas@cc.uoi.gr
URL: http://www.math.uoi.gr/~sntouyas

Abstract:

In this paper we prove existence results for semilinear stochastic neutral functional differential systems with unbounded delay in abstract space. Our theory makes use of analytic semigroups and fractional power of closed operators and Sadovskii fixed point theorem.

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Paper's Title:

The Conservativeness of Girsanov Transformed for Symmetric Jump-diffusion Process

Author(s):

Mila Kurniawaty and Marjono

Department of Mathematics,
Universitas Brawijaya,
Malang,
Indonesia.
E-mail: mila_n12@ub.ac.id, marjono@ub.ac.id

Abstract:

We study about the Girsanov transformed for symmetric Markov processes with jumps associated with regular Dirichlet form. We prove the conservativeness of it by dividing the regular Dirichlet form  into the "small jump" part and the "big jump" part.

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Paper's Title:

Fekete Szegö problem on the Class of Bazilevič functions B₁(α) related to the Lemniscate Bernoulli

Author(s):

N. M. Asih, Marjono, Sa'adatul Fitri, Ratno Bagus Edy Wibowo

Department of Mathematics,
University of Brawijaya,
Malang 65145,
Indonesia.
Department of Mathematics,
University of Udayana,
Bali,
Indonesia.
E-mail: madeasih@unud.ac.id

Department of Mathematics,
University of Brawijaya,
Malang 65145,
Indonesia.
E-mail: marjono@ub.ac.id

Department of Mathematics,
University of Brawijaya,
Malang 65145,
Indonesia.
E-mail: saadatulfitri@ub.ac.id

Department of Mathematics,
University of Brawijaya,
Malang 65145,
Indonesia.
E-mail: rbagus@ub.ac.id

Abstract:

We provide a sharp boundaries inequalities for Fekete Szegö problem |a₃-μ a₂²|, the coefficients of logarithmic function log~ f(z)/z, and the coefficients of the inverse function f(f'(w)) on the Bazilevič functions B₁(α) related to the Lemniscate Bernoulli on the unit disk D={z: |z| < 1}. We obtained the result by using some properties of function with positive real part relates to coefficients problems.

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Paper's Title:

High Order Collocation Method for the Generalized Kuramoto-Sivashinsky Equation

Author(s):

Zanele Mkhize, Nabendra Parumasur and Pravin Singh

School of Mathematics, Statistics and Computer Sciences,
University of KwaZulu-Natal,
Private Bag X 54001,
Durban 4000.
E-mail: mkhizez2@ukzn.ac.za
parumasurn1@ukzn.ac.za
 singhp@ukzn.ac.za
URL: https://www.ukzn.ac.za

Abstract:

In this paper, we derive the heptic Hermite basis functions and use them as basis functions in the orthogonal collocation on finite elements (OCFE) method. We apply the method to solve the generalized Kuramoto-Sivashinsky equation. Various numerical simulations are presented to justify the computational efficiency of the proposed method.

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23: Paper Source PDF document

Paper's Title:

Generalized Composition Operators On Besov Spaces

Author(s):

Vishal Sharma, Sanjay Kumar and Stanzin Dolkar

Department of Mathematics,
Central University of Jammu,
Jammu and Kashmir,
India.
E-mail: sharmavishal911@gmail.com

 
Department of Mathematics,
Central University of Jammu,
Jammu and Kashmir,
India.
E-mail:  sanjaykmath@gmail.com

Department of Mathematics,
Central University of Jammu,
Jammu and Kashmir,
India.
E-mail: stanzin.math@cujammu.ac.in

 

Abstract:

In this paper, we characterize boundedness, compactness and find the essential norm estimates for generalized composition operators between Besov spaces and  S_p  spaces.

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Paper's Title:

Iterative Approximation of Common Fixed Points of a Finite Family of Asymptotically Hemi-contractive Type Mappings

Author(s):

Jui-Chi Huang

Center for General Education,
Northern Taiwan Institute of Science and Technology,
Peito, Taipei,
Taiwan, 11202, R.O.C.
juichi@ntist.edu.tw

Abstract:

In this paper, we prove that the sequence of the modified Ishikawa-Xu,
Ishikawa-Liu, Mann-Xu and Mann-Liu iterative types of a finite family of
asymptotically hemi-contractive type mappings converges strongly to a common
fixed point of the family in a real p-uniformly convex Banach space with
p>1. Our results improve and extend some recent results.

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Paper's Title:

A Nonlinear Proximal Alternating Directions Method for Structured Variational Inequalities

Author(s):

M. Li

Department of Management Science and Engineering, School of Economics and Management
Southeast University, Nanjing, 210096,
China.
liminnju@yahoo.com

Abstract:

In this paper, we present a nonlinear proximal alternating directions method (NPADM) for solving a class of structured variational inequalities (SVI). By choosing suitable Bregman functions, we generalize the proximal alternating directions method proposed by He, et al.. The convergence of the method is proved under quite mild assumptions and flexible parameter conditions.

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22: Paper Source PDF document

Paper's Title:

Analysis of the Dynamic Response of the Soil-pile Behavioral Model Under Lateral Load

Author(s):

Ibrahima Mbaye, Mamadou Diop, Aliou Sonko and Malick Ba

University of Thies,
Department of Mathematics, Bp 967 Thies,
Senegal.
E-mail: imbaye@univ-thies.sn
mamadou.diop@univ-thies.sn
aliousonko59@gmail.com
mmalickba@hotmail.fr
URL: https://www.univ-thies.sn
 

Abstract:

This work aims to extend and improve our previous study on mathematical and numerical analysis of stationary Pasternak model. In this paper a dynamic response of Pasternak model is considered. On the one hand we establish the existence and uniqueness of the solution by using the Lax-Milgram theorem and the spectral theory thus the existence of a Hilbert basis is shown and the spectral decomposition of any solution of the problem can be established and on the other hand the finite element method is used to determinate the numerical results. Furthermore, the influence of soil parameters G_p and K_p on the displacement of the pious is studied numerically at any time t_n.

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Paper's Title:

A Self Adaptive Method for Solving Split Bilevel Variational Inequalities Problem in Hilbert Spaces

Author(s):

Francis Akutsah¹, Ojen Kumar Narain², Funmilayo Abibat Kasali³ Olawale Kazeem Oyewole⁴ and Akindele Adebayo Mebawondu⁵

¹School of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: 216040405@stu.ukzn.ac.za, akutsah@gmail.com

²School of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa. 
E-mail: naraino@ukzn.ac.za

³Mountain Top University,
Prayer City, Ogun State,
Nigeria.
E-mail: fkasali@mtu.edu.ng

⁴Technion-Israel Institute of Technology.
E-mail: 217079141@stu.ukzn.ac.za, oyewoleolawalekazeem@gmail.co

⁵School of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa. 
DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS),
Johannesburg,
South Africa.
Mountain Top University,
Prayer City, Ogun State,
Nigeria.
E-mail: dele@aims.ac.za

Abstract:

In this work, we study the split bilevel variational inequality problem in two real Hilbert spaces. We propose a new modified inertial projection and contraction method for solving the aforementioned problem when one of the operators is pseudomonotone and Lipschitz continuous while the other operator is α-strongly monotone. The use of the weakly sequential continuity condition on the Pseudomonotone operator is removed in this work. A Strong convergence theorem of the proposed method is proved under some mild conditions. In addition, some numerical experiments are presented to show the efficiency and implementation of our method in comparison with other methods in the literature in the framework of infinite dimensional Hilbert spaces. The results obtained in this paper extend, generalize and improve several.

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Paper's Title:

On Infinite Unions and Intersections of Sets in a Metric Space

Author(s):

Spiros Konstantogiannis

Ronin Institute,
Montclair, New Jersey,
United States.
E-mail: spiros.konstantogiannis@ronininstitute.org
URL: https://www.researchgate.net/profile/Spiros-Konstantogiannis

Abstract:

The aim of this paper is to examine infinite unions and intersections of sets in a general metric space, with a view to explaining when an infinite intersection of open sets is an open set and when an infinite union of closed sets is a closed set.

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Paper's Title:

Reconstruction of Discontinuities of Functions Given Noisy Data

Author(s):

Eric D. Mbakop

67A Beaver Park Rd,
Framingham, MA, 01702,
U. S. A.
ericsteve86@yahoo.fr

Abstract:

Suppose one is given noisy data of a discontinuous piecewise-smooth function along with a bound on its second derivative. The locations of the points of discontinuity of f and their jump sizes are not assumed known, but are instead retrieved stably from the noisy data. The novelty of this paper is a numerical method that allows one to locate some of these points of discontinuity with an accuracy that can be made arbitrarily small.

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21: Paper Source PDF document

Paper's Title:

Para-chaotic Tuples of Operators

Author(s):

Bahmann Yousefi and Javad Izadi

Department of Mathematics,
Payame Noor University,
P.O. Box 19395-3697, Tehran,
Iran
b_yousefi@pnu.ac.ir
javadie2003@yahoo.com

Abstract:

In this paper, we introduce para-chaotic tuples of operators and we give some relations between para-chaoticity and Hypercyclicity Criterion for a tuple of operators.

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21: Paper Source PDF document

Paper's Title:

A Review on Minimally Supported Frequency Wavelets

Author(s):

K Pallavi¹, M C Lineesh¹, A Noufal²

¹Department of Mathematics,
National Institute of Technology Calicut,
Kerala 673601,
India.
E-mail:  pavikrishnakumar@gmail.com
lineesh@nitc.ac.in

²Department of Mathematics,
Cochin University of Science and Technology,
Kerala 682022,
India.
E-mail: noufal@cusat.ac.in

Abstract:

This paper provides a review on Minimally Supported Frequency (MSF) wavelets that includes the construction and characterization of MSF wavelets. The characterization of MSF wavelets induced from an MRA is discussed and the nature of the low-pass filter associated with it is explained. The concept of wavelet set and dimension function is introduced to study this class of wavelets. Along with MSF wavelets, s-elementary wavelets and unimodular wavelets are also considered due to the similarity in definitions. Examples and illustrations are provided for more clarity.

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21: Paper Source PDF document

Paper's Title:

Li-Yorke and Expansivity for Composition Operators on Lorentz Space

Author(s):

Rajat Singh and Romesh Kumar

Department of Mathematics,
University of Jammu,
Jammu 180006,
INDIA.
E-mail: rajat.singh.rs634@gmail.com

Department of Mathematics,
University of Jammu,
Jammu 180006,
INDIA.
E-mail: romeshmath@gmail.com

Abstract:

In this paper, we investigate Li-Yorke composition operators and some of its variations on Lorentz spaces. Further, we also study expansive composition operators on these spaces. The work of the paper is essentially based on the work in [3], [6], [8] and [15].

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20: Paper Source PDF document

Paper's Title:

Stability of Almost Multiplicative Functionals

Author(s):

Norio Niwa, Hirokazu Oka, Takeshi Miura and Sin-Ei Takahasi

Faculty of Engineering, Osaka Electro-Communication University,
Neyagawa 572-8530,
Japan

Faculty of Engineering, Ibaraki University,
Hitachi 316-8511,
Japan

Department of Applied Mathematics and Physics, Graduate School of Science and Engineering,
Yamagata University,
Yonezawa 992-8510
Japan

oka@mx.ibaraki.ac.jp
miura@yz.yamagata-u.ac.jp
sin-ei@emperor.yz.yamagata-u.ac.jp

Abstract:

Let δ and p be non-negative real numbers. Let be the real or complex number field and a normed algebra over . If a mapping satisfies

then we show that φ is multiplicative or for all If, in addition, φ satisfies

for some p≠1, then by using Hyers-Ulam-Rassias stability of additive Cauchy equation, we show that φ is a ring homomorphism or for all In other words, φ is a ring homomorphism, or an approximately zero mapping. The results of this paper are inspired by Th.M. Rassias' stability theorem.

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20: Paper Source PDF document

Paper's Title:

Szegö Limits and Haar Wavelet Basis

Author(s):

M. N. N. Namboodiri and S. Remadevi

Dept. of Mathematics, Cochin University of Science and Technology,
Cochin-21, Kerala,
India.

nambu@cusat.ac.in

Dept. of Mathematics, College of Engineering,
Cherthala, Kerala,
India.

rema@mec.ac.in
 

Abstract:

This paper deals with Szegö type limits for multiplication operators on L² (R) with respect to Haar orthonormal basis. Similar studies have been carried out by Morrison for multiplication operators T_f using Walsh System and Legendre polynomials [14]. Unlike the Walsh and Fourier basis functions, the Haar basis functions are local in nature. It is observed that Szegö type limit exist for a class of multiplication operators T_f , f∈ L^∞ (R) with respect to Haar (wavelet) system with appropriate ordering. More general classes of orderings of Haar system are identified for which the Szegö type limit exist for certain classes of multiplication operators. Some illustrative examples are also provided.

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20: Paper Source PDF document

Paper's Title:

Polyanalytic Functions on Subsets of Z[i]

Author(s):

Abtin Daghighi

Linköping University,
SE-581 83,
Sweden.

E-mail: abtindaghighi@gmail.com

Abstract:

For positive integers q we consider the kernel of the powers L^q where L is one of three kinds of discrete analogues of the Cauchy-Riemann operator. The first two kinds are well-studied, but the third kind less so. We give motivations for further study of the third kind especially since its symmetry makes it more appealing for the cases q≥ 2.

From an algebraic perspective it makes sense that the chosen multiplication on the kernels is compatible with the choice of pseudo-powers. We propose such multiplications together with associated pseudo-powers. We develop a proof-tool in terms of certain sets of uniqueness.

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Paper's Title:

Optimization Techniques on Affine Differential Manifolds

Author(s):

Ali S Rasheed, Faik Mayah and Ahmed A H AL-Jumaili

Ministry of Higher Education and Scientific Research,
Iraq.
E-mail: ahmedhashem@gmail.com
 

Department of Physics, College of Sciences,
University of Wasit,
Iraq.
E-mail: faik.mayah@gmail.com
 

Abstract:

In addition to solid ground of Riemannian manifolds fundamentals, this article interviews some popular optimization methods on Riemannian manifolds. Several optimization problems can be better stated on manifolds rather than Euclidean space, such as interior point methods, which in turns based on self-concordant functions (logarithmic barrier functions). Optimization schemes like the steepest descent scheme, the Newton scheme, and others can be extended to Riemannian manifolds. This paper introduces some Riemannian and non-Riemannian schemes on manifolds.

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Paper's Title:

Optimal Control Analysis of HIV/AIDS Epidemic Model with an Antiretroviral Treatment

Author(s):

U. Habibah and R. A. Sari

Mathematics Department and Reseach Group of Biomathematics,
Faculty of Mathematics and Natural Science,
Brawijaya University, Jl. Veteran Malang 65145,
Indonesia.
E-mail: ummu_habibah@ub.ac.id
 

Abstract:

A mathematical model of HIV/AIDS is governed by a system of ordinary differential equations in the presence of an antiretroviral treatment (ARV). The theory of optimal control is applied to an epidemic model of HIV/AIDS which an ARV is used as a control strategy in order to prevent the spread of HIV/AIDS. The optimality system is derived by applying the Pontryagin's Minimum Principle. We analyze the boundedness and positivity of solutions, and an existence of the optimal control. Numerical simulations are conducted to obtain numerical solution of the optimally system.

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20: Paper Source PDF document

Paper's Title:

Existence of Solution of Differential and Riemann-Liouville Equation Via Fixed Point Approach in Complex Valued b-Metric Spaces

Author(s):

K. Afassinou, A. A. Mebawondu, H. A. Abass and O. K. Narain

Department of Science Access,
University of Zululand, KwaDlangezwa,
South Africa.
E-mail: komia@aims.ac.za

DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS),
Johannesburg,
South Africa.
E-mail: dele@aims.ac.za

DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS),
Johannesburg,
South Africa.
E-mail: hammedabass548@gmail.com

School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: naraino@ukzn.ac.za

Abstract:

In this paper, we establish some fixed point and common fixed point results for a new type of generalized contractive mapping using the notion of C-class function in the framework of complex valued b-metric spaces. As an application, we establish the existence and uniqueness of a solution for Riemann-Liouville integral and ordinary differential equation in the framework of a complete complex valued b-metric spaces. The obtained results generalize and improve some fixed point results in the literature.

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Paper's Title:

An Integration Technique for Evaluating Quadratic Harmonic Sums

Author(s):

J. M. Campbell and K.-W. Chen

Department of Mathematics and Statistics,
York University, 4700 Keele St, Toronto,
ON M3J 1P3,
Canada.
E-mail: jmaxwellcampbell@gmail.com

Department of Mathematics, University of Taipei,
  No. 1, Ai-Guo West Road,
Taipei 10048, Taiwan.
E-mail: kwchen@uTaipei.edu.tw
URL: https://math.utaipei.edu.tw/p/412-1082-22.php

Abstract:

The modified Abel lemma on summation by parts has been applied in many ways recently to determine closed-form evaluations for infinite series involving generalized harmonic numbers with an upper parameter of two. We build upon such results using an integration technique that we apply to ``convert'' a given evaluation for such a series into an evaluation for a corresponding series involving squared harmonic numbers.

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20: Paper Source PDF document

Paper's Title:

Portfolio Optimization of Sharia and Non-Sharia Stocks Using Single Index Model (Case study: Jakarta Sharia Index and Kompas 100 Index)

Author(s):

Kwardiniya Andawaningtyas, Muhammad Luthfi, Marjono, Endang Wahyu Handamari, Umu S'adah, Evi Ardiyani

Department of Mathematics,
Brawijaya University, Malang,
Indonesia.

Department of Mathematics,
IPB University, Bogor,
Indonesia.

E-mail: dina_math@ub.ac.id
muhammadluthfi@student.ub.ac.id
marjono@ub.ac.id
ewahyu-math@ub.ac.id
u.saadah@ub.ac.id
ardiyanievi@apps.ipb.ac.id

Abstract:

Stocks are instruments with high returns but also have increased risks. One way to overcome this risk is to form a stock portfolio. This study observed 30 sharia stocks listed on the Jakarta Islamic Index (JII) and 28 non-shariah stocks listed on the Kompas 100 Index from March 2020 to September 2022. The data used is the daily closing price of stocks, the number of stock dividends, and the daily closing price of the Jakarta Composite Index (JCI) from 3rd March 2020, to 31st August 2022. In addition, interest rate of Bank Indonesia Certificate (SBI) is used as risk-free rate. This study aims to optimize the sharia and non-sharia stocks portfolio using the Single Index Model (SIM), which will then be evaluated using the Sharpe, Treynor, and Jensen ratio. The result is that the optimal portfolio of sharia stocks have better performance than the optimal portfolio of non-sharia stocks based on the Treynor ratio. Meanwhile, the optimal portfolio of non-sharia stocks have better performance than the optimal portfolio of sharia stocks based on the Sharpe and Jensen ratio.

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Paper's Title:

Approximation of Common Fixed Points of a Finite Family of Asymptotically Demicontractive Mappings in Banach Spaces

Author(s):

Yuchao Tang, Yong Cai, Liqun Hu and Liwei Liu

 Department of Mathematics, NanChang University,
Nanchang 330031, P.R. China
 Department of Mathematics, Xi'an Jiaotong University,
Xi'an 710049, P.R. China

hhaaoo1331@yahoo.com.cn
 

Abstract:

By virtue of new analytic techniques, we analyze and study
several strong convergence theorems for the approximation of
common fixed points of asymptotically demicontractive mappings
via the multistep iterative sequence with errors in Banach
spaces. Our results improve and extend the corresponding ones
announced by Osilike , Osilike and Aniagbosor, Igbokwe, Cho et
al., Moore and Nnoli, Hu and all the others.

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Paper's Title:

Traub-Potra-Type Method for Set-Valued Maps

Author(s):

Ioannis K. Argyros and Saïd Hilout

Cameron University,
Department of Mathematics Sciences,
Lawton, OK 73505,
USA

iargyros@cameron.edu

URL: http://www.cameron.edu/~ioannisa/

Poitiers University,
Laboratoire de Mathematiques et Applications,
Bd. Pierre et Marie Curie, Teleport 2, B.P. 30179,
86962 Futuroscope Chasseneuil Cedex,
France

said.hilout@math.univ-poitiers.fr

http://www-math.univ-poitiers.fr/~hilout/

Abstract:

We introduce a new iterative method for approximating a locally unique solution of variational inclusions in Banach spaces by using generalized divided differences of the first order. This method extends a method considered by Traub  (in the scalar case) and by Potra  (in the Banach spaces case) for solving nonlinear equations to variational inclusions. An existence-convergence theorem and a radius of convergence are given under some conditions on divided differences operator and Lipschitz-like continuity property of set-valued mappings. The R-order of the method is equal to the unique positive root of a certain cubic equation, which is $1.839..., and as such it compares favorably to related methods such as the Secant method which is only of order $1.618....

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Paper's Title:

Composite Variational-Like Inequalities Given By Weakly Relaxed ζ-Semi-Pseudomonotone Multi-Valued Mapping

Author(s):

Syed Shakaib Irfan, Iqbal Ahmad, Zubair Khan and Preeti Shukla

College of Engineering, Qassim University
Buraidah, Al-Qassim,
Saudi Arabia.
E-mail: shakaib@qec.edu.sa

College of Engineering, Qassim University
Buraidah, Al-Qassim,
Saudi Arabia.
E-mail: iqbal@qec.edu.sa

Department of Mathematics,
Integral University Lucknow,
India.
E-mail: zkhan@iul.ac.in

Department of Mathematics,
Integral University Lucknow,
India.
E-mail: shuklapreeti1991@gmail.com

 

Abstract:

In this article, we introduce a composite variational-like inequalities with weakly relaxed ζ-pseudomonotone multi-valued maping in reflexive Banach spaces. We obtain existence of solutions to the composite variational-like inequalities with weakly relaxed ζ-pseudomon -otone multi-valued maps in reflexive Banach spaces by using KKM theorem. We have also checked the solvability of the composite variational-like inequalities with weakly relaxed ζ-semi-pseudomonotone multi-valued maps in arbitrary Banach spaces using Kakutani-Fan-Glicksberg fixed point theorem.

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Paper's Title:

On Ruled Surfaces According to Quasi-Frame in Euclidean 3-Space

Author(s):

M. Khalifa Saad and R. A. Abdel-Baky

Department of Mathematics, Faculty of Science,
Islamic University of Madinah,
KSA.
Department of Mathematics, Faculty of Science,
Sohag University, Sohag,
EGYPT.
E-mail: mohamed_khalifa77@science.sohag.edu.eg, mohammed.khalifa@iu.edu.sa

Department of Mathematics, Faculty of Science,
Assiut University, Assiut,
EGYPT.
E-mail: rbaky@live.com

Abstract:

This paper aims to study the skew ruled surfaces by using the quasi-frame of Smarandache curves in the Euclidean 3-space. Also, we reveal the relationship between Serret-Frenet and quasi-frames and give a parametric representation of a directional ruled surface using the quasi-frame. Besides, some comparative examples are given and plotted which support our method and main results.

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Paper's Title:

A New Method with Regularization for Solving Split Variational Inequality Problems in Real Hilbert Spaces

Author(s):

Francis Akutsah¹ and Ojen Kumar Narain²

¹School of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: 216040405@stu.ukzn.ac.za, akutsah@gmail.com

 ²School of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: naraino@ukzn.ac.za

Abstract:

In this paper, we introduce a new inertial extrapolation method with regularization for approximating solutions of split variational inequality problems in the frame work of real Hilbert spaces. We prove that the proposed method converges strongly to a minimum-norm solution of the problem without using the conventional two cases approach. In addition, we present some numerical experiments to show the efficiency and applicability of the proposed method. The results obtained in this paper extend, generalize and improve several results in this direction.

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Paper's Title:

Uniqueness Problems for Difference Polynomials Sharing a Non-Zero Polynomial of Certain Degree With Finite Weight

Author(s):

V. Priyanka, S. Rajeshwari and V. Husna

Department of Mathematics,
School of Engineering,
Presidency University,
Bangalore-560064,
India.
E-mail: priyapriyankaram1994@gmail.com rajeshwaripreetham@gmail.com
husnav43@gmail.com

Abstract:

In this paper, we prove a result on the value distribution of difference polynomials sharing higher order derivatives of meromorphic functions which improves some earlier results. At the same time, we also prove possible uniqueness relation of entire functions when the difference polynomial generated by them sharing a non zero polynomial of certain degree. The result obtained in the paper will improve and generalize a number of recent results in a compact and convenient way.

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Paper's Title:

SQIRV Model for Omicron Variant with Time Delay

Author(s):

S. Dickson, S. Padmasekaran, G. E. Chatzarakis and S. L. Panetsos

Mathematics, Periyar University, Periyar Palkalai Nagar, Salem,
636011, Tamilnadu,
India.
E-mail: dickson@periyaruniversity.ac.in, padmasekarans@periyaruniversity.ac.in

Electrical and Electronic Engineering Educators, School of
Pedagogical and Technological Education (ASPETE),
Marousi 15122, Athens,
Greece.
E-mail: geaxatz@otenet.gr, spanetsos@aspete.gr

Abstract:

In order to examine the dynamics of the Omicron variant, this paper uses mathematical modelling and analysis of a SQIRV model, taking into account the delay in the conversion of susceptible individuals into infected individuals and infected individuals into recovered individuals. The pandemic was eventually controlled as a result of the massive delays. To assure the safety of the host population, this concept incorporates quarantine and the COVID-19 vaccine. Both local and global stability of the model are examined. It is found that the fundamental reproduction number affects both local and global stability conditions. Our findings show that asymptomatic cases caused by an affected population play an important role in increasing Omicron infection in the general population. The most recent data on the pandemic Omicron variant from Tamil Nadu, India, is verified.

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Paper's Title:

Approximately Dual p-Approximate Schauder Frames

Author(s):

K. Mahesh Krishna and P. Sam Johnson

Stat-Math Unit, Indian Statistical Institute, Bangalore Centre,
Karnataka 560 059
India.

Department of Mathematical and Computational Sciences,
National Institute of Technology Karnataka (NITK),
Surathkal, Mangaluru 575 025,
India.

E-mail: kmaheshak@gmail.com sam@nitk.edu.in
 

Abstract:

Approximately dual frame in Hilbert spaces was introduced by Christensen and Laugesen to overcome difficulties in constructing dual frames for a given Hilbert space frame. It becomes even more difficult in Banach spaces to construct duals. For this purpose, we introduce approximately dual frames for a class of approximate Schauder frames for Banach spaces and develop basic theory. Approximate dual for this subclass is completely characterized and its perturbation is also studied.

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Paper's Title:

Finite Volume Approximation of a Class of 2D Elliptic Equations with Discontinuous and Highly Oscillating Coefficients

Author(s):

J. D. Bambi Pemba and B. Ondami

Université Marien Ngouabi
Factuté des Sciences et Techniques
BP 69 Brazzaville,
Congo.
E-mail: bondami@gmail.com
URL: https://www.researchgate.net/profile/Bienvenu-Ondami
https://www.linkedin.com/in/bienvenu-ondami

Abstract:

In this paper, we are interested in the Finite Volume approximation of a second-order two-dimensional elliptic equation in heterogeneous porous medium with a periodic structure. The equation's coefficients are therefore discontinuous and highly oscillating. This class of problems has been extensively studied in the literature, where various methods proposed for determining the so-called homogenized problem. What we are particularly interested in is the direct numerical approximation of the problem, which has received little attention in the literature. We use the cell-centered finite volume approach for this purpose. Error estimates are established, and numerical simulations are conducted for both the isotropic and anisotropic media cases. The obtained solution is compared to the homogenized solution, and the results show that this approach provides an adequate approximation of the exact solution.

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Paper's Title:

A New Iterative Approximation of a Split Fixed Point Constraint Equilibrium Problem

Author(s):

Musa Adewale Olona¹, Adhir Maharaj² and Ojen Kumar Narain³

¹School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: 219095783@stu.ukzn.ac.za

²Department of Mathematics,
Durban University of Technology, Durban,
South Africa.
E-mail: adhirm@dut.ac.za

³School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: naraino@ukzn.ac.za

Abstract:

The purpose of this paper is to introduce an iterative algorithm for approximating an element in the solution set of the common split feasibility problem for fixed points of demimetric mappings and equilibrium problem for monotone mapping in real Hilbert spaces. Motivated by self-adaptive step size method, we incorporate the inertial technique to accelerate the convergence of the proposed method and establish a strong convergence of the sequence generated by the proposed algorithm. Finally, we present a numerical example to illustrate the significant performance of our method. Our results extend and improve some existing results in the literature.

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Paper's Title:

Asymptotic Inequalities for the Maximum Modulus of the Derivative of a Polynomial

Author(s):

Clément Frappier

Département de Mathématiques et de Génie industriel École Polytechnique de Montréal,
C.P.~6079, succ. Centre-ville Montréal (Québec),
H3C 3A7, CANADA

clement.frappier@polymtl.ca.

 

Abstract:

Let be an algebraic polynomial of degree ≤n, and let ∥p∥= max {|p(z)|:|z| = 1}. We study the asymptotic behavior of the best possible constant φn,k (R), for k = 0 and k=1, in the inequality ∥p'(Rz)∥ + φn,k (R) |a_k| ≤ nR^n-1 ∥p∥, R → ∞.

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Paper's Title:

A New Method for Comparing Closed Intervals

Author(s):

Ibraheem Alolyan

Department of Mathematics, College of Sciences,
King Saud University, P. O. Box 2455, Riyadh 11451,
Saudi Arabia

ialolyan@ksu.edu.sa
URL:http://faculty.ksu.edu.sa/ALolyan
 

Abstract:

The usual ordering ``≤" on R is a total ordering, that is, for any two real numbers in R, we can determine their order without difficulty. However, for any two closed intervals in R, there is not a natural ordering among the set of all closed intervals in R. Several methods have been developed to compare two intervals. In this paper, we define the μ-ordering which is a new method for ordering closed intervals.

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Paper's Title:

Numerical Solution of A System of Singularly Perturbed Convection-Diffusion Boundary-Value Problems Using Mesh Equidistribution Technique

Author(s):

Pratibhamoy Das and Srinivasan Natesan

Department of Mathematics,
Indian Institute of Technology Guwahati,
Guwahati - 781 039,
India.

pratibhamoy@gmail.com
natesan@iitg.ernet.in
URL: http://www.iitg.ernet.in/natesan/

Abstract:

In this article, we consider a system of singularly perturbed weakly coupled convection-diffusion equations having diffusion parameters of different magnitudes. These small parameters give rise to boundary layers. An upwind finite difference scheme on adaptively generated mesh is used to obtain a suitable monitor function that gives first-order convergence which is robust with respect to the diffusion parameters. We present the results of numerical experiments for linear and semilinear system of differential equations to support the effectiveness of our preferred monitor function obtained from theoretical analysis.

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Paper's Title:

Some Properties of the Marshall-Olkin and Generalized Cuadras-Augé Families of Copulas

Author(s):

Edward Dobrowolski and Pranesh Kumar

Department of Mathematics and Statistics
University of Northern British Columbia
Prince George, BC,
Canada, V2N 4Z9

E-mail: Pranesh.Kumar@unbc.ca  

Abstract:

We investigate some properties of the families of two parameter Marshall-Olkin and Generalized Cuadras-Augé copulas. Some new results are proved for copula parameters, dependence measure and mutual information. A numerical application is discussed.

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Paper's Title:

On Some Constructive Method of Rational Approximation

Author(s):

Vasiliy A. Prokhorov

Department of Mathematics and Statistics
University of South Alabama
Mobile, Alabama 36688-0002,
USA.

E-mail: prokhoro@southalabama.edu
URL: http://www.southalabama.edu/mathstat/people/prokhorov.shtml

Abstract:

We study a constructive method of rational approximation of analytic functions based on ideas of the theory of Hankel operators. Some properties of the corresponding Hankel operator are investigated. We also consider questions related to the convergence of rational approximants. Analogues of Montessus de Ballore's and Gonchars's theorems on the convergence of rows of Padé approximants are proved.

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Paper's Title:

The Effect of Harvesting Activities on Prey-Predator Fishery Model with Holling type II in Toxicant Aquatic Ecosystem

Author(s):

Moh Nurul Huda, Fidia Deny Tisna Amijaya, Ika Purnamasari

Department of Mathematics, Faculty of Mathematics and Natural Science,
Mulawarman University,
Samarinda, East Kalimantan,75123
Indonesia.
E-mail: muh.nurulhuda@fmipa.unmul.ac.id
 fidiadta@fmipa.unmul.ac.id
ika.purnamasari@fmipa.unmul.ac.id

Abstract:

This paper discussed prey-predator fishery models, in particular by analysing the effects of toxic substances on aquatic ecosystems. It is assumed in this model, that the prey population is plankton and the predator population is fish.\ Interaction between the two populations uses the Holling type II function. The existence of local and global critical points of the system are shown and their stability properties are analysed. Furthermore, Bionomic equilibrium and optimal control of harvesting are discussed. Finally, numerical simulations have been carried out to show in the interpretation of results.

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Paper's Title:

Coexisting Attractors and Bubbling Route to Chaos in Modified Coupled Duffing Oscillators

Author(s):

B. Deruni¹, A. S. Hacinliyan^1,2, E. Kandiran³, A. C. Keles², S. Kaouache⁴, M.-S. Abdelouahab⁴, N.-E. Hamri⁴

¹Department of Physics,
University of Yeditepe,
Turkey.

²Department of Information Systems and Technologies,
University of Yeditepe,
Turkey

³Department of Software Development,
University of Yeditepe,
Turkey.

⁴Laboratory of Mathematics and their interactions,
University Center of Abdelhafid Boussouf,
Mila 43000,
Algeria.

E-mail: berc890@gmail.com
ahacinliyan@yeditepe.edu.tr
engin.kandiran@yeditepe.edu.tr
cihan.keles@yeditepe.edu.tr
s.kaouache@centr-univ-mila.dz
medsalah3@yahoo.fr
n.hamri@centre-univ-mila.dz

Abstract:

In this article dynamical behavior of coupled Duffing oscillators is analyzed under a small modification. The oscillators have cubic damping instead of linear one. Although single duffing oscillator has complex dynamics, coupled duffing systems possess a much more complex structure. The dynamical behavior of the system is investigated both numerically and analytically. Numerical results indicate that the system has double scroll attractor with suitable parameter values. On the other hand, bifurcation diagrams illustrate rich behavior of the system, and it is seen that, system enters into chaos with different routes. Beside classical bifurcations, bubbling route to chaos is observed for suitable parameter settings. On the other hand, Multistability of the system is indicated with the coexisting attractors, such that under same parameter setting the system shows different periodic and chaotic attractors. Moreover, chaotic synchronization of coupled oscillators is illustrated in final section.

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17: Paper Source PDF document

Paper's Title:

Conservativeness Criteria of Girsanov Transformation for Non-Symmetric Jump-diffusion

Author(s):

Mila Kurniawaty

DDepartment of Mathematics,
Universitas Brawijaya, Malang,
Indonesia.
E-mail: mila_n12@ub.ac.id

Abstract:

We develop the condition in our previous paper [The Conservativeness of Girsanov transformed for symmetric jump-diffusion process (2018)] in the framework of nonsymmetric Markov process with jumps associated with regular Dirichlet form. We prove the conservativeness of it by relation in duality of Girsanov transformed process and recurrent criteria of Dirichlet form.

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17: Paper Source PDF document

Paper's Title:

Bicomplex Univalent Functions

Author(s):

Mohd Arif, Amjad Ali, Rajat Singh^* and Romesh Kumar

Department of Mathematics,
University of Jammu,
Jammu And Kashmir,
India.
E-mail: azizymaths@gmail.com

Department of Mathematics,
University of Jammu,
Jammu And Kashmir,
India.
E-mail: amjadladakhi687@gmail.com

Department of Mathematics,
University of Jammu,
Jammu And Kashmir,
India.
E-mail: ^*rajat.singh.rs634@gmail.com

Department of Mathematics,
University of Jammu,
Jammu And Kashmir,
India.
E-mail: romeshmath@gmail.com

Abstract:

In this paper we introduce bicomplex univalent functions and also discuss the properties of a specific class of univalent functions.

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17: Paper Source PDF document

Paper's Title:

Fractional Integral Inequalities of Hermite-Hadamard Type for P-convex and Quasi-Convex Stochastic Process

Author(s):

Oualid Rholam, Mohammed Barmaki and Driss Gretet

National School of Applied Sciences (ENSA),
University Ibn Tofail,
B.P 242 Kenitra 14000,
phone number : +212606257757,
Morocco.
E-mail: oualid.rholam@uit.ac.ma

 
Science Faculty Ben M'sik,
University Hassan II,
B.P 7955 Av Driss El Harti Sidi Othmane 20700,
phone number : +212 5 22 70 46 71 ,
Morocco.
E-mail:  mohammed.barmaki@uit.ac.ma

National School of Applied Sciences (ENSA),
University Ibn Tofail,
B.P 242 Kenitra 14000,
phone number : +212661403557,
Morocco.
E-mail: driss.gretete@uit.ac.ma 

 

Abstract:

In this paper we consider the class of P-convex and Quasi-convex stochastic processes on witch we apply a general class of generalized fractional integral operator in order to establish new integral inequalities of Hermite-Hadammard type. then we obtain some results for well known types of fractional integrals. Results obtained in this paper may be starting point as well as a useful source of inspiration for further research in convex analysis.

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16: Paper Source PDF document

Paper's Title:

An Easy and Efficient Way for Solving A class of Singular Two Point Boundary Value Problems

Author(s):

Muhammed I. Syam, Muhammed N. Anwar and Basem S. Attili

Mathematical Sciences Department
United Arab Emirates University, P. O. Box 17551
Al-Ain, United Arab Emirates
b.attili@uaeu.ac.ae

Abstract:

We will consider an efficient and easy way for solving a certain class of singular two point boundary value problems. We will employ the least squares method which proved to be efficient for this type of problems. Enough examples that were considered by others will be solved with comparison with the results presented there.

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16: Paper Source PDF document

Paper's Title:

1-type Pseudo-Chebyshev Subspaces in Generalized 2-normed Spaces

Author(s):

Sh. Rezapour

Department of Mathematics, Azarbaijan University of Tarbiat Moallem,
Azarshahr, Tabriz,
Iran
sh.rezapour@azaruniv.edu

Abstract:

We construct a generalized 2-normed space from every normed space. We introduce 1-type pseudo-Chebyshev subspaces in generalized 2-normed spaces and give some results in this field.

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16: Paper Source PDF document

Paper's Title:

Product Formulas Involving Gauss Hypergeometric Functions

Author(s):

Edward Neuman

Department of Mathematics, Mailcode 4408,
Southern Illinois University,
1245 Lincoln Drive,
Carbondale, IL 62901,
USA.
edneuman@math.siu.edu
URL: http://www.math.siu.edu/neuman/personal.html

Abstract:

New formulas for a product of two Gauss hypergeometric functions are derived. Applications to special functions, with emphasis on Jacobi polynomials, Jacobi functions, and Bessel functions of the first kind, are included. Most of the results are obtained with the aid of the double Dirichlet average of a univariate function.

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16: Paper Source PDF document

Paper's Title:

Regular Variation on Time Scales and Dynamic Equations

Author(s):

Pavel Řehák

Institute of Mathematics, Academy of Sciences of the Czech Republic
Žižkova 22, CZ61662 Brno,
Czech Republic
rehak@math.muni.cz
URL:http://www.math.muni.cz/~rehak

Abstract:

The purpose of this paper is twofold. First, we want to initiate a study of regular variation on time scales by introducing this concept in such a way that it unifies and extends well studied continuous and discrete cases. Some basic properties of regularly varying functions on time scales will be established as well. Second, we give conditions under which certain solutions of linear second order dynamic equations are regularly varying. Open problems and possible directions for a future research are discussed, too.

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16: Paper Source PDF document

Paper's Title:

Purely Unrectifiable Sets with Large Projections

Author(s):

Harold R. Parks

Department of Mathematics, Oregon State University,
Corvallis, Oregon 97331--4605,
USA
parks@math.oregonstate.edu
URL: http://www.math.oregonstate.edu/people/view/parks/

Abstract:

For n≥2, we give a construction of a compact subset of that is dispersed enough that it is purely unrectifiable, but that nonetheless has an orthogonal projection that hits every point of an (n-1)-dimensional unit cube. Moreover, this subset has the additional surprising property that the orthogonal projection onto any straight line in is a set of positive 1-dimensional Hausdorff measure.

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16: Paper Source PDF document

Paper's Title:

Shape Diagrams for 2D Compact Sets - Part II: Analytic Simply Connected Sets.

Author(s):

S. Rivollier, J. Debayle and J.-C. Pinoli

Ecole Nationale Supérieure des Mines de Saint-Etienne,

CIS - LPMG, UMR CNRS 5148, 158 cours Fauriel,

42023 Saint-Etienne Cedex 2, France.

 rivollier@emse.fr; debayle@emse.fr; pinoli@emse.fr
 

Abstract:

Shape diagrams are representations in the Euclidean plane introduced to study 3-dimensional and 2-dimensional compact convex sets. However, they can also been applied to more general compact sets than compact convex sets. A compact set is represented by a point within a shape diagram whose coordinates are morphometrical functionals defined as normalized ratios of geometrical functionals. Classically, the geometrical functionals are the area, the perimeter, the radii of the inscribed and circumscribed circles, and the minimum and maximum Feret diameters. They allow twenty-two shape diagrams to be built. Starting from these six classical geometrical functionals, a detailed comparative study has been performed in order to analyze the representation relevance and discrimination power of these twenty-two shape diagrams. The first part of this study is published in a previous paper 16. It focused on analytic compact convex sets. A set will be called analytic if its boundary is piecewise defined by explicit functions in such a way that the six geometrical functionals can be straightforwardly calculated. The purpose of this paper is to present the second part, by focusing on analytic simply connected compact sets. The third part of the comparative study is published in a following paper 17. It is focused on convexity discrimination for analytic and discretized simply connected compact sets.

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16: Paper Source PDF document

Paper's Title:

On an Elliptic Over-Determined Problem in Dimension Two

Author(s):

Lakhdar Ragoub
Department of Mathematics and Information of Tiyadhechnology
AL Yamamah University
P.O. Box 45 180, Riyadh 11 512
Saudi Arabia.

lragoub@yu.edu.sa

 

Abstract:

We extend the method of Weinberger for a non-linear over-determined elliptic problem
in R². We prove that the domain in consideration is a ball. The tool of this investigation are maximum principles and P-functions.

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16: Paper Source PDF document

Paper's Title:

Bilinear Regular Operators on Quasi-Normed Functional Spaces

Author(s):

D. L. Fernandez and E. B. Silva

Universidade Estadual de Campinas - Unicamp
Instituto de Matematica
Campinas - SP
Brazil.
E-mail: dicesar@ime.unicamp.br

Universidade Estadual de Maringa--UEM
Departamento de Matematica
Av.~Colombo 5790
Maringa - PR
Brazil.
E-mail: ebsilva@uem.br

Abstract:

Positive and regular bilinear operators on quasi-normed functional spaces are introduced and theorems characterizing compactness of these operators are proved. Relations between bilinear operators and their adjoints in normed functional spaces are also studied.

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16: Paper Source PDF document

Paper's Title:

Analysis of a Frictional Contact Problem for Viscoelastic Piezoelectric Materials

Author(s):

Meziane Said Ameur, Tedjani Hadj Ammar and Laid Maiza

Departement of Mathematics,
El Oued University,
P.O. Box 789, 39000 El Oued,
Algeria.
E-mail: said-ameur-meziane@univ-eloued.dz

Departement of Mathematics,
El Oued University,
P.O. Box 789, 39000 El Oued,
Algeria.
E-mail: hadjammar-tedjani@univ-eloued.dz

Department of Mathematics,
Kasdi Merbah University,
30000 Ouargla,
Algeria.
E-mail: maiza.laid@univ-ouargla.dz

 

Abstract:

In this paper, we consider a mathematical model that describes the quasi-static process of contact between two thermo-electro-viscoelastic bodies with damage and adhesion. The damage of the materials caused by elastic deformations. The contact is frictional and modeled with a normal compliance condition involving adhesion effect of contact surfaces. Evolution of the bonding field is described by a first order differential equation. We derive variational formulation for the model and prove an existence and uniqueness result of the weak solution. The proof is based on arguments of evolutionary variational inequalities, parabolic inequalities, differential equations, and fixed point theorem.

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16: Paper Source PDF document

Paper's Title:

On Subspace-Supercyclic Operators

Author(s):

Mansooreh Moosapoor

Assistant Professor,
Department of Mathematics,
Farhangian University, Tehran,
Iran.
E-mail: mosapor110@gmail.com m.mosapour@cfu.ac.ir

Abstract:

In this paper, we prove that supercyclic operators are subspace-supercyclic and by this we give a positive answer to a question posed in ( L. Zhang, Z. H. Zhou, Notes about subspace-supercyclic operators, Ann. Funct. Anal., 6 (2015), pp. 60--68). We give examples of subspace-supercyclic operators that are not subspace-hypercyclic. We state that if T is an invertible supercyclic operator then Tⁿ and T^-n is subspace-supercyclic for any positive integer n. We give two subspace-supercyclicity criteria. Surprisingly, we show that subspace-supercyclic operators exist on finite-dimensional spaces.

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16: Paper Source PDF document

Paper's Title:

Two Geometric Constants Related to Isosceles Orthogonality on Banach Space

Author(s):

Huayou Xie, Qi Liu and Yongjin Li

Department of Mathematics,
Sun Yat-sen University,
 Guangzhou, 510275,
P. R. China.
E-mail: xiehy33@mail2.sysu.edu.cn

Department of Mathematics,
Sun Yat-sen University,
 Guangzhou, 510275,
P. R. China.
E-mail: liuq325@mail2.sysu.edu.cn

Department of Mathematics,
Sun Yat-sen University,
 Guangzhou, 510275,
P. R. China.
E-mail: stslyj@mail.sysu.edu.cn

Abstract:

In this paper, we introduce new geometric constant C(X,a_i,b_i,c_i,2) to measure the difference between isosceles orthogonality and special Carlsson orthogonalities. At the same time, we also present the geometric constant C(X,a_i,b_i,c_i), which is a generalization of the rectangular constant proposed by Joly. According to the inequality on isosceles orthogonality, we give the boundary characterization of these geometric constants. Then the relationship between these geometric constants and uniformly non-square property can also be discussed. Furthermore, we show that there is a close relationship between these geometric constants and some important geometric constants.

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16: Paper Source PDF document

Paper's Title:

Eigenvalue Bounds based on Projections

Author(s):

Pravin Singh, Shivani Singh, Virath Singh

University of KwaZulu-Natal,
Private Bag X54001,
Durban, 4001,
South Africa.

University of South Africa,
Department of Decision Sciences, PO Box 392,
 Pretoria,0003,
South Africa.

University of KwaZulu-Natal,
Private Bag X54001,
Durban, 4001,
South Africa.

E-mail: singhp@ukzn.ac.za, singhs2@unisa.ac.za, singhv@ukzn.ac.za
 

Abstract:

In this paper, we derive expressions for the bounds of the extremal eigenvalues of positive definite matrices. Our approach is to use a symmetric projection operator onto an n-2 dimensional subspace of the real space of n tuples. These bounds are based on traces of the matrix and its powers. They are relatively easy and inexpensive to compute.

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15: Paper Source PDF document

Paper's Title:

Isoperimetric Inequalities for Dual Harmonic Quermassintegrals

Author(s):

Yuan Jun, Zao Lingzhi and Duan Xibo

School of Mathematics and Computer Science,
Nanjing Normal University, Nanjing, 210097,
China.
yuanjun_math@126.com

Department of Mathematics, Nanjing Xiaozhuang University,
Nanjing, 211171,
China.
lzhzhao@163.com

Department of Mathematics, Shandong Water Polytechnic,
Shandong, 276826,
China
dxb1111@sohu.com

Abstract:

In this paper, some isoperimetric inequalities for the dual harmonic quermassintegrals are established.

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15: Paper Source PDF document

Paper's Title:

On the Convergence in Law of Iterates of Random-Valued Functions

Author(s):

Karol Baron

Uniwersytet Śląski, Instytut Matematyki
 Bankowa 14, PL--40--007 Katowice,
Poland
baron@us.edu.pl

Abstract:

Given a probability space (Ω, A, P) a separable and complete metric space X with the σ-algebra B of all its Borel subsets and a B A -measurable f : X * Ω → X we consider its iterates fⁿ, n N, defined on X * Ω^N by f¹(x,ω) = f(x,ω₁)  and fⁿ⁺¹(x,ω)=f(fⁿ(x,ω),ω_n+1), provide a simple criterion for the convergence in law of fⁿ(x,·)) _{n N}, to a random variable independent of x X , and apply this criterion to linear functional equations in a single variable.

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15: Paper Source PDF document

Paper's Title:

Shape Diagrams for 2D Compact Sets - Part I: Analytic Convex Sets.

Author(s):

S. Rivollier, J. Debayle and J.-C. Pinoli

Ecole Nationale Supérieure des Mines de Saint-Etienne,

CIS - LPMG, UMR CNRS 5148, 158 cours Fauriel,

42023 Saint-Etienne Cedex 2, France.

 rivollier@emse.fr; debayle@emse.fr; pinoli@emse.fr
 

Abstract:

Shape diagrams are representations in the Euclidean plane introduced to study 3-dimensional and 2-dimensional compact convex sets. Such a set is represented by a point within a shape diagram whose coordinates are morphometrical functionals defined as normalized ratios of geometrical functionals. Classically, the geometrical functionals are the area, the perimeter, the radii of the inscribed and circumscribed circles, and the minimum and maximum Feret diameters. They allow thirty-one shape diagrams to be built. Most of these shape diagrams can also been applied to more general compact sets than compact convex sets. Starting from these six classical geometrical functionals, a detailed comparative study has been performed in order to analyze the representation relevance and discrimination power of these thirty-one shape diagrams. The purpose of this paper is to present the first part of this study, by focusing on analytic compact convex sets. A set will be called analytic if its boundary is piecewise defined by explicit functions in such a way that the six geometrical functionals can be straightforwardly calculated. The second and third part of the comparative study are published in two following papers [19.20]. They are focused on analytic simply connected sets and convexity discrimination for analytic and discretized simply connected sets, respectively.

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15: Paper Source PDF document

Paper's Title:

The Influence of Fluid Pressure in Macromechanical Cochlear Model

Author(s):

F. E. Aboulkhouatem¹, F. Kouilily¹, N. Achtaich¹, N. Yousfi¹ and M. El Khasmi²

¹Department of Mathematics and Computer Science, Faculty of Sciences
Ben M'sik, Hassan II University, Casablanca,
Morocco.

²Department of Biology, Faculty of Sciences
Ben M'sik, Hassan II University, Casablanca,
Morocco.

E-mail: fatiaboulkhouatem@gemail.com
URL: http://www.fsb.univh2c.ma/

Abstract:

An increase of pressure in the structure of cochlea may cause a hearing loss. In this paper, we established the relationship between the fluid pressure and the amplitude of displacement of Basilar Membrane to clarify the mechanisms of hearing loss caused by increasing of this pressure. So, a mathematical cochlear model was formulated using finite difference method in order to explain and demonstrate this malfunction in passive model. Numerical simulations may be considered as helpful tools which may extend and complete the understanding of a cochlea dysfunction.

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15: Paper Source PDF document

Paper's Title:

Formulation of Approximate Mathematical Model for Incoming Water to Some Dams on Tigris and Euphrates Rivers Using Spline Function

Author(s):

Nadia M. J. Ibrahem, Heba A. Abd Al-Razak, and Muna M. Mustafa

Mathematics Department,
College of Sciences for Women,
University of Baghdad, Baghdad,
Iraq.
E-mail: Nadiamj_math@csw.uobaghdad.edu.iq

Abstract:

In this paper, we formulate three mathematical models using spline functions, such as linear, quadratic and cubic functions to approximate the mathematical model for incoming water to some dams. We will implement this model on dams of both rivers; dams on the Tigris are Mosul and Amara while dams on the Euphrates are Hadetha and Al-Hindya.

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15: Paper Source PDF document

Paper's Title:

Some fixed point results in partial S-metric spaces

Author(s):

M. M. Rezaee, S. Sedghi, A. Mukheimer, K. Abodayeh, and Z. D. Mitrovic

Department of Mathematics, Qaemshahr Branch,
Islamic Azad University, Qaemshahr,
Iran.
E-mail: Rezaee.mohammad.m@gmail.com

Department of Mathematics, Qaemshahr Branch,
Islamic Azad University, Qaemshahr,
Iran.
E-mail: sedghi.gh@qaemiau.ac.ir

Department of Mathematics and General Sciences,
Prince Sultan University, Riyadh,
KSA.
E-mail: mukheimer@psu.edu.sa

Department of Mathematics and General Sciences,
Prince Sultan University, Riyadh,
KSA.
E-mail: kamal@psu.edu.sa

Nonlinear Analysis Research Group,
Faculty of Mathematics and Statistics,
Ton Duc Thang University, Ho Chi Minh City,
Vietnam.
E-mail: zoran.mitrovic@tdtu.edu.vn

Abstract:

We introduce in this article a new class of generalized metric spaces, called partial S-metric spaces. In addition, we also give some interesting results on fixed points in the partial S-metric spaces and some applications.

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15: Paper Source PDF document

Paper's Title:

Several Applications of a Local Non-convex Young-type Inequality

Author(s):

Loredana Ciurdariu, Sorin Lugojan

Department of Mathematics,
"Politehnica" University of Timisoara,
P-ta. Victoriei, No.2, 300006-Timisoara,
Romania.

E-mail: ltirtirau87@yahoo.com

Abstract:

A local version of the Young inequality for positive numbers is used in order to deduce some inequalities about determinants and norms for real quadratic matrices and norms of positive operators on complex Hilbert spaces.

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15: Paper Source PDF document

Paper's Title:

Fractional exp(-φ(ξ))- Expansion Method and its Application to Space--Time Nonlinear Fractional Equations

Author(s):

A. A. Moussa and L. A. Alhakim

Department of Management Information System and Production Management,
College of Business and Economics, Qassim University,
P.O. BOX 6666, Buraidah: 51452,
Saudi Arabia.
E-mail: Alaamath81@gmail.com
URL: https://scholar.google.com/citations?user=ccztZdsAAAAJ&hl=ar

Department of Management Information System and Production Management,
College of Business and Economics, Qassim University,
P.O. BOX 6666, Buraidah: 51452,
Saudi Arabia.
E-mail: Lama2736@gmail.com
URL: https://scholar.google.com/citations?user=OSiSh1AAAAAJ&hl=ar

Abstract:

In this paper, we mainly suggest a new method that depends on the fractional derivative proposed by Katugampola for solving nonlinear fractional partial differential equations. Using this method, we obtained numerous useful and surprising solutions for the space--time fractional nonlinear Whitham--Broer--Kaup equations and space--time fractional generalized nonlinear Hirota--Satsuma coupled KdV equations. The solutions obtained varied between hyperbolic, trigonometric, and rational functions, and we hope those interested in the real-life applications of the previous two equations will find this approach useful.

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15: Paper Source PDF document

Paper's Title:

A Fuzzy Soft Quotient Topology and Its Properties

Author(s):

Haripamyu, Riri Alfakhriati, Monika Rianti Helmi, Jenizon

Department of Mathematics and Data Science, Andalas University, Padang, Indonesia.
E-mail: haripamyu@sci.unand.ac.id
ririalfakhriati123@gmail.com
monikariantihelmi@sci.unand.ac.id
jenizon@gmail.com

Abstract:

This research is to construct a new topology on fuzzy soft set by using the concept of quotient topology. Then we study the concept of quotient map to define the fuzzy soft quotient map and provide some relevant properties of fuzzy soft quotient map. Furthermore, we give some examples related to fuzzy soft quotient topology and fuzzy soft quotient map to apply some properties of fuzzy soft quotient map.

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15: Paper Source PDF document

Paper's Title:

On Statistically Φ-Convergence

Author(s):

Supama

Department of Mathematics,
Gadjah Mada University,
Yogyakarta 55281,
Indonesia.
E-mail: supama@ugm.ac.id

Abstract:

The idea of statistical convergence was introduced by Antoni Zygmund in 1935. Based on in the idea of Zygmund, Henry Fast and Hugo Steinhaus independently introduced a concept of statistical convergence as a generalization of an ordinary convergence in the same year 1951. In this paper, by using the Orlicz function, we introduce a concept of statistical Φ-convergence, as a generalization of the statistical convergence. Further, we observe some basic properties and some topological properties of the statistical Φ-convergent sequences

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14: Paper Source PDF document

Paper's Title:

Stability Problems for Generalized Additive Mappings and Euler-Lagrange Type Mappings

Author(s):

M. Todoroki, K. Kumahara, T. Miura and S.-E. Takahasi

The Open University of Japan,
Chiba, 261-8586,
Japan
tomamiyu3232@sky.sannet.ne.jp
kumahara@ouj.ac.jp

 Yamagata University,
Yonezawa 992-8510,
Japan
miura@yz.yamagata-u.ac.jp

Toho University, Yamagata University,
Chiba, 273-0866,
Japan
sin_ei1@yahoo.co.jp

Abstract:

We introduce a generalized additivity of a mapping between Banach spaces and establish the Ulam type stability problem for a generalized additive mapping. The obtained results are somewhat different from the Ulam type stability result of Euler-Lagrange type mappings obtained by H. -M. Kim, K. -W. Jun and J. M. Rassias.

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14: Paper Source PDF document

Paper's Title:

New Inequalities of Mill's Ratio and Application to The Inverse Q-function Approximation

Author(s):

Pingyi Fan

Department of Electronic Engineering,
Tsinghua University, Beijing,
China

fpy@tsinghua.edu.cn

Abstract:

In this paper, we investigate the Mill's ratio estimation problem and get two new inequalities. Compared to the well known results obtained by Gordon, they becomes tighter. Furthermore, we also discuss the inverse Q-function approximation problem and present some useful results on the inverse solution. Numerical results confirm the validness of our theoretical analysis. In addition, we also present a conjecture on the bounds of inverse solution on Q-function.

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14: Paper Source PDF document

Paper's Title:

Asymptotic Analysis of Positive Decreasing Solutions of a Class of Systems of Second Order Nonlinear Differential Equations in the Framework of Regular Variation

Author(s):

Jaroslav Jaroš, Kusano Takaŝi, Tomoyuki Tanigawa

Department of Mathematical Analysis and Numerical Mathematics,
Faculty of Mathematics, Physics and Informatics,
Comenius Universiy, 842 48 Bratislava,
Slovakia.

E-mail: ksntksjm4@gmail.com

Professor Emeritus at: Hiroshima University,
Department of Mathematics, Faculty of Science,
Higashi-Hiroshima 739-8526,
Japan.

E-mail: jaros@fmph.uniba.sk

Department of Mathematics, Faculty of Education,
Kumamoto University, Kumamoto 860-8555,
Japan.

E-mail: tanigawa@educ.kumamoto-u.ac.jp
 

Abstract:

The system of nonlinear differential equations

is under consideration, where α_i and β_i are positive constants and p_i(t) and q_i(t) are continuous regularly varying functions on [a,∞). Two kinds of criteria are established for the existence of strongly decreasing regularly varying solutions with negative indices of (A) with precise asymptotic behavior at infinity. Fixed point techniques and basic theory of regular variation are utilized for this purpose.

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14: Paper Source PDF document

Paper's Title:

Countable Ordinal Spaces and Compact Countable Subsets of a Metric Space

Author(s):

B. Alvarez-Samaniego, A. Merino

Nucleo de Investigadores Cientificos
Facultad de Ciencias,
Universidad Central del Ecuador (UCE)
Quito,
Ecuador.
E-mail: borys_yamil@yahoo.com, balvarez@uce.edu.ec

Escuela de Ciencias Fisicas y Matematica
Facultad de Ciencias Exactas y Naturales
Pontificia Universidad Catolica del Ecuador
Apartado: 17-01-2184, Quito,
Ecuador.
E-mail: aemerinot@puce.edu.ec

Abstract:

We show in detail that every compact countable subset of a metric space is homeomorphic to a countable ordinal number, which extends a result given by Mazurkiewicz and Sierpinski for finite-dimensional Euclidean spaces. In order to achieve this goal, we use Transfinite Induction to construct a specific homeomorphism. In addition, we prove that for all metric space, the cardinality of the set of all the equivalence classes, up to homeomorphisms, of compact countable subsets of this metric space is less than or equal to aleph-one. We also show that for all cardinal number smaller than or equal to aleph-one, there exists a metric space with cardinality equals the aforementioned cardinal number.

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14: Paper Source PDF document

Paper's Title:

The Higher Coefficients for Bazilevic Functions B₁(α)

Author(s):

Marjono, Sa'adatul Fitri, and Krisna Adilia Daniswara

Department of Mathematics,
Faculty of Mathematics and Natural Sciences,,
Brawijaya University, Malang Jawa Timur 65145
Indonesia.
E-mail: marjono@ub.ac.id
saadatulfitri@ub.ac.id
krisnaadiliadaniswara@gmail.com
 

Abstract:

Let f be analytic in D{z: |z|< 1} with , and normalized by the conditions f(0)=f'(0)-1=0. We give sharp estimates for the seventh and eighth coefficients for the class of Bazilevic functions with logarithmic growth, B₁α, defined by for α≥0.

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14: Paper Source PDF document

Paper's Title:

Reduced Generalized Combination Synchronization Between Two n-Dimensional Integer-Order Hyperchaotic Systems and One m-Dimensional Fractional-Order Chaotic System

Author(s):

Smail Kaouache, Mohammed Salah Abdelouahab and Rabah Bououden

Laboratory of Mathematics and their interactions,
Abdelhafid Boussouf University Center, Mila.
Algeria
E-mail: smailkaouache@gmail.com, medsalah3@yahoo.fr, rabouden@yahoo.fr

Abstract:

This paper is devoted to investigate the problem of reduced generalized combination synchronization (RGCS) between two n-dimensional integer-order hyperchaotic drive systems and one m-dimensional fractional-order chaotic response system. According to the stability theorem of fractional-order linear system, an active mode controller is proposed to accomplish this end. Moreover, the proposed synchronization scheme is applied to synchronize three different chaotic systems, which are the Danca hyperchaotic system, the modified hyperchaotic Rossler system, and the fractional-order Rabinovich-Fabrikant chaotic system. Finally, numerical results are presented to fit our theoretical analysis.

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Paper's Title:

Complete Analysis of Global Behavior of Certain System of Piecewise Linear Difference Equations

Author(s):

Atiratch Laoharenoo, Ratinan Boonklurb and Watcharapol Rewlirdsirikul

Department of Mathematics and Computer Science,
Kamnoetvidya Science Academy, Rayong 21210
Thailand.
E-mail: atiratch.l@kvis.ac.th

 
Department of Mathematics and Computer Science,
Faculty of Science, Chulalongkorn University, Bangkok 10330
Thailand.
E-mail: ratinan.b@chula.ac.th

Department of Mathematics and Computer Science,
Faculty of Science, Chulalongkorn University, Bangkok 10330
Thailand.
E-mail: 6570104323@student.chula.ac.th

 

Abstract:

Our goal is to study the system of piecewise linear difference equations x_{n+1} = |x_n|-y_n-b and y_{n+1} = x_n - |y_n| + 1 where n ≥ 0 and b ≥ 6. We can prove that the behavior of the solution can be divided into 2 types depending on the region of initial condition (x₀,y₀). That is, the solution eventually becomes the equilibrium point. Otherwise, the solution eventually becomes the periodic solution of prime period 5. All regions of initial condition for each type of solution are determined.

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Paper's Title:

Jordan Canonical Form of Interval Matrices and Applications

Author(s):

S. Hema Surya, T. Nirmala and K. Ganesan

Department of Mathematics, College of Engineering and Technology,
SRM Institute of Science and Technology,
Kattankulathur,
Chennai-603203,
India.
E-mail: nirmalat@srmist.edu.in
URL: https://www.srmist.edu.in/faculty/dr-t-nirmala/

Abstract:

A square interval matrix over R can be converted to diagonal form if certain prerequisites are satisfied. However not all square matrices can be diagonalized. As a consequence, we strive the next simplest form to which it can be reduced while retaining important properties such as eigenvalues, rank, nullity, and so on. It turns out that any real interval matrix has a Jordan Canonical Form (JCF) over E if it has n interval eigenvalues in IR. We discuss in this paper a method for computing the Jordan canonical form of an interval matrix using a new pairing technique and a new type of interval arithmetic that will make classifying and analyzing interval matrices easier and more efficient. We conclude with a numerical example that supports the theory and application of predator-prey model.

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Paper's Title:

A Reverse of the Triangle Inequality in Inner Product Spaces and Applications for Polynomials

Author(s):

I. Brnetić, S. S. Dragomir, R. Hoxha and J. Pečarić

Department of Applied Mathematics, Faculty of Electrical Engineering and Computing,
University of Zagreb, Unska 3, 10 000 Zagreb,
Croatia
andrea@zpm.fer.hr

School of Computer Science & Mathematics, Victoria University
Po Box 14428, Melbourne Vic 8001
Australia
sever.dragomir@vu.edu.au
URL:http://rgmia.vu.edu.au/dragomir

Faculty of Applied Technical Sciences, University of Prishtina,
Mother Theresa 5, 38 000 Prishtina
Kosova
razimhoxha@yahoo.com

Faculty of Textile Technology, University of Zagreb,
Pierottijeva 6, 10000 Zagreb,
Croatia
pecaric@hazu.hr

Abstract:

A reverse of the triangle inequality in inner product spaces related to the celebrated Diaz-Metcalf inequality with applications for complex polynomials is given.

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Paper's Title:

On the Generalized Stability and Asymptotic Behavior of Quadratic Mappings

Author(s):

Hark-Mahn Kim, Sang-Baek Lee and Eunyoung Son

Department of Mathematics
Chungnam National University
Daejeon, 305-764,
Republic of Korea
hmkim@cnu.ac.kr

Abstract:

We extend the stability of quadratic mappings to the stability of general quadratic mappings with several variables, and then obtain an improved asymptotic property of quadratic mappings on restricted domains.

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Paper's Title:

Ergodic Solenoidal Homology II: Density of Ergodic Solenoids

Author(s):

Vicente Muñoz and Ricardo Pérez Marco

Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM,
 Serrano 113 bis, 28006 Madrid,
Spain
 and
Facultad de Matemáticas, Universidad Complutense de Madrid,
 Plaza de Ciencias 3, 28040 Madrid,
Spain

CNRS, LAGA UMR 7539, Université Paris XIII,
99 Avenue J.-B. Cl\'ement, 93430-Villetaneuse,
France

vicente.munoz@imaff.cfmac.csic.es
ricardo@math.univ-paris13.fr

Abstract:

A measured solenoid is a laminated space endowed with a tranversal measure invariant by holonomy. A measured solenoid immersed in a smooth manifold produces a closed current (known as a generalized Ruelle-Sullivan current). Uniquely ergodic solenoids are those for which there is a unique (up to scalars) transversal measure. It is known that for any smooth manifold, any real homology class is represented by a uniquely ergodic solenoid. In this paper, we prove that the currents associated to uniquely ergodic solenoids are dense in the space of closed currents, therefore proving the abundance of such objects.

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Paper's Title:

On the product of M-measures in l-groups

Author(s):

A. Boccuto, B. Riěcan, and A. R. Sambucini

Dipartimento di Matematica e Informatica,
via Vanvitelli, 1 I-06123 Perugia,
Italy.
 boccuto@dipmat.unipg.it
 URL: http://www.dipmat.unipg.it/~boccuto

 Katedra Matematiky, Fakulta Prírodných Vied,
Univerzita Mateja Bela,
Tajovského, 40, Sk-97401 Banská Bystrica,
Slovakia.
 riecan@fpv.umb.sk

 Dipartimento di Matematica e Informatica,
via Vanvitelli, 1 I-06123 Perugia,
Italy.
 matears1@unipg.it
 URL: http://www.unipg.it/~matears1

 

Abstract:

Some extension-type theorems and compactness properties for the
product of l-group-valued M-measures are proved.

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Paper's Title:

Solving Fractional Transport Equation via Walsh Function

Author(s):

A. Kadem

L. M. F. N., Mathematics Department,
 University of Setif,
Algeria
abdelouahak@yahoo.fr
 

Abstract:

In this paper we give a complete proof of A method for the solution of fractional transport equation in three-dimensional case by using Walsh function is presented. The main characteristic of this technique is that it reduces these problems to those of solving a system of algebraic equations, thus greatly simplifying the problem.

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Paper's Title:

Existence Results for Second Order Impulsive Functional Differential Equations with Infinite Delay

Author(s):

M. Lakrib, A. Oumansour and K. Yadi  

Laboratoire de Mathématiques, Université Djillali
Liabées, B.P. 89 Sidi Bel Abbès 22000, Algérie
mlakrib@univ-sba.dz
oumansour@univ-sba.dz

Laboratoire de Mathématiques, Université Abou Bekr
Belkaid, B.P. 119 Tlemcen 13000, Algérie
k_yadi@mail.univ-tlemcen.dz

Abstract:

In this paper we study the existence of solutions for second order impulsive functional differential equations with infinite delay. To obtain our results, we apply fixed point methods.

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Paper's Title:

On an Autocorrection Phenomenon of the Eckhoff Interpolation

Author(s):

A. Poghosyan  

Institute of Mathematics, National Academy of Sciences,
24b Marshal Baghramian ave., Yerevan 0019,
Republic of Armenia
arnak@instmath.sci.am
 

Abstract:

The paper considers the Krylov-Lanczos and the Eckhoff interpolations of a function with a discontinuity at a known point. These interpolations are based on certain corrections associated with jumps in the first derivatives. In the Eckhoff interpolation, approximation of the exact jumps is accomplished by the solution of a system of linear equations. We show that in the regions where the 2-periodic extension of the interpolated function is smooth, the Eckhoff interpolation converges faster compared with the Krylov-Lanczos interpolation. This accelerated convergence is known as the autocorrection phenomenon. The paper presents a theoretical explanation of this phenomenon. Numerical experiments confirm theoretical estimates.

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Paper's Title:

Positive Solutions to a System of Boundary Value Problems for Higher-Dimensional Dynamic Equations on Time Scales

Author(s):

I. Y. Karaca

Department of Mathematics,
Ege University,
35100 Bornova, Izmir,
Turkey

ilkay.karaca@ege.edu.tr

URL: http://ege.edu.tr
 

Abstract:

In this paper, we consider the system of boundary value problems for higher-dimensional dynamic equations on time scales. We establish criteria for the existence of at least one or two positive solutions. We shall also obtain criteria which lead to nonexistence of positive solutions. Examples applying our results are also given.

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Paper's Title:

Harmonic Functions with Positive Real Part

Author(s):

Sïbel Yalçin

Uludag Universitesi,
Fen Edebiyat Fakultesi, Matematik Bolumu,
16059 Bursa,
Turkey

syalcin@uludag.edu.tr

Abstract:

In this paper, the class of harmonic functions f=h+{g} with positive real part and normalized by f(ζ )=1, (|ζ|<1) is studied, where h and g are analytic in U={z:|z|<1}. Some properties of this class are searched. Sharp coefficient relations are given for functions in this class. On the other hand, the author make use of Alexander integral transforms of certain analytic functions (which are starlike with respect to f(ζ)) with a view to investigating the construction of sense preserving, univalent and close to convex harmonic functions.

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Paper's Title:

Some Functional Inequalities for the Geometric Operator Mean

Author(s):

Mustapha Raissouli

Taibah University, Faculty of Sciences, Department of Mathematics,
Al Madinah Al Munawwarah, P.O.Box 30097,
Kingdom of Saudi Arabia.

raissouli_10@hotmail.com

Abstract:

In this paper, we give some new inequalities of functional type for the power geometric operator mean involving several arguments.

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Paper's Title:

A Nonhomogeneous Subdiffusion Heat Equation

Author(s):

Joel-Arturo Rodriguez-Ceballos, Ana-Magnolia Marin, Ruben-Dario Ortiz

Instituto Tecnológico de Morelia,
Morelia, Michoacan,
Mexico

E-mail: joel@ifm.umich.mx

Universidad de Cartagena,
Campus San Pablo,
Cartagena de Indias, Bolivar,
Colombia

E-mail: amarinr@unicartagena.edu.co

E-mail:  joel@ifm.umich.mx

Abstract:

In this paper we consider a nonhomogeneous subdiffusion heat equation of fractional order with Dirichlet boundary conditions.

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Paper's Title:

Wavelet Frames in Higher Dimensional Sobolev Spaces

Author(s):

Raj Kumar, Manish Chauhan, and Reena

Department of Mathematics,
Kirori Mal College, University of Delhi,
New Delhi-110007,
India.
E-mail: rajkmc@gmail.com

Department of Mathematics,
University of Delhi,
New Delhi-110007,
India
E-mail: manish17102021@gmail.com

Department of Mathematics,
Hans Raj College, University of Delhi,
New Delhi-110007,
India
E-mail: reena.bhagwat29@gmail.com

Abstract:

In this paper, we present sufficient condition for the sequence of vectors to be a frame for H^s(R^d) are derived. Necessary and sufficient conditions for the sequence of vectors to be tight wavelet frames in H^s(R^d) are obtained. Further, as an application an example of tight wavelet frames for H^s(R²) as bivariate box spline over 3-direction are given.

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Paper's Title:

Convergence and Stability Results for New Three Step Iteration Process in Modular Spaces

Author(s):

Naresh Kumar and Renu Chugh

Department of Mathematics,
M.D. University,
Rohtak-124001, Haryana,
India.
E-mail: nks280@gmail.com
E-mail: chugh.r1@gmail.com

Abstract:

The aim of this paper is to introduce a new iteration process (5) for ρ-contraction mappings in Modular spaces. We obtain some analytical proof for convergence and stability of our iteration process (5). We show that our iteration process (5) gives faster convergence results than the leading AK iteration process (4) for contraction mappings. Moreover, a numerical example (using the Matlab Software) is presented to compare the rate of convergence for existing iteration processes with our new iteration process (5).

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Paper's Title:

Hankel Operators on Copson's Spaces

Author(s):

Nicolae Popa

Institute of Mathematics of Romanian Academy,
P.O. BOX 1-764 RO-014700 Bucharest,
Romania.

E-mail: Nicolae.Popa@imar.ro, npopafoc@gmail.com

Abstract:

We give a characterization of boundedness of a Hankel matrix, generated by a pozitive decreasing sequence, acting on Copson's space cop(2).

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Paper's Title:

On a subset of Bazilevic functions

Author(s):

Marjono and D. K. Thomas

Department of Mathematics,
Faculty of Mathematics and Natural Sciences,
Brawajaya University,
Malang, Jawa Timur 65145,
Indonesia.
E-mail: marjono@ub.ac.id

Department of Mathematics,
Swansea University, Singleton Park,
Swansea, SA2 8PP,
United Kingdom.
E-mail: d.k.thomas@swansea.ac.uk

Abstract:

Let S denote the class of analytic and univalent functions in of the form For α≥0, the subclass B₁α of S of Bazilevic functions has been extensively studied. In this paper we determine various properties of a subclass of B₁α, for α≥0 which extends early results of a class of starlike functions studied by Ram Singh.

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Paper's Title:

Nonlinear System of Mixed Ordered Variational Inclusions Involving XOR Operation

Author(s):

Iqbal Ahmad, Abdullah and Syed Shakaib Irfan

Department of Mechanical Engineering,
College of Engineering, Qassim University
Buraidah 51452, Al-Qassim,
Saudi Arabia.
E-mail: iqbal@qec.edu.sa, i.ahmad@qu.edu.sa

Zakir Husain Delhi College,
University of Delhi,
JLN Marg, New Delhi- 110 002,
India.
E-mail: abdullahdu@qec.edu.sa

Department of Mathematics,
Aligarh Muslim University, Aligarh,
India.
E-mail: shakaibirfan@gmail.com

Abstract:

In this work, we introduce and solve an NSMOVI frameworks system involving XOR operation with the help of a proposed iterative algorithm in real ordered positive Hilbert spaces. We discuss the existence of a solution of a considered system of inclusions involving XOR operation by applying the resolvent operator technique with XOR operation and also study the strong convergence of the sequences generated by the considered algorithm. Further, we give a numerical example in support of our considered problem which gives the grantee that all the proposed conditions of our main result are fulfilled.

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Paper's Title:

Lie Group Theoretic Approach of One-Dimensional Black-Scholes Equation

Author(s):

P. L. Zondi and M. B. Matadi

Department of Mathematical sciences,
Faculty of Sciences & Agriculture, University of Zululand,
P Bag X1001, Kwa-Dlangezwa 3886,
South Africa.
E-mail: matadim@unizulu.ac.za
zondip@unizulu.ac.za

Abstract:

This study discusses the Lie Symmetry Analysis of Black-Scholes equation via a modified local one-parameter transformations. It can be argued that the transformation of the Black-Scholes equation is firstly obtained by means of riskless rate. Thereafter, the corresponding determining equations to the reduced equation are found. Furthermore, new symmetries of the Black-Scholes equation are constructed and lead to invariant solutions.

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Paper's Title:

Linear System of Singularly Perturbed Initial Value Problems with Robin Initial Conditions

Author(s):

S. Dinesh, G. E. Chatzarakis, S. L. Panetsos and S. Sivamani

Department of Mathematics,
Saranathan College of Engineering,
Tiruchirappalli-620012,
Tamil Nadu,
India.

Department of Electrical and Electronic Engineering Educators,
School of Pedagogical and Technological Education,
Marousi 15122, Athens,
Greece.

E-mail: geaxatz@otenet.gr, dineshselvaraj24@gmail.com,
spanetsos@aspete.gr, winmayi2012@gmail.com

Abstract:

On the interval (0,1], this paper considers an initial value problem for a system of n singularly perturbed differential equations with Robin initial conditions. On a piecewise uniform Shishkin mesh, a computational approach based on a classical finite difference scheme is proposed. This approach is shown to be first-order convergent in the maximum norm uniformly in the perturbation parameters. The theory is illustrated by a numerical example.

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Paper's Title:

A General Fractional Control Scheme for Compound Combination Synchronization Between Different Fractional-Order Identical Chaotic Systems

Author(s):

Soumia Bensimessaoud and Smail Kaouache

Laboratory of Mathematics and their interactions, Abdelhafid Boussouf University Center, Mila, Algeria.
E-mail: soumiabensimessaoud@gmail.com, smailkaouache@gmail.com

Abstract:

In this paper, we aim to investigate the problem of compound combination synchronization (CCS) between four different fractional-order identical chaotic systems. Based on Laplace transformation and stability theory of linear dynamical systems, a new control law is proposed to assure the achievement of this kind of synchronization. Secondly, this control scheme is applied to realised CCS between four identical unified chaotic systems. Recall, that the proposed control scheme can be applied to wide classes of chaotic and hyperchaotic systems. Numerical simulations are given to show the effectiveness of the proposed method.

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Paper's Title:

The successive approximations method and error estimation in terms of at most the first derivative for delay ordinary differential equations

Author(s):

Alexandru Mihai Bica

Department of Mathematics,
University of Oradea,
Str. Armatei Romane no.5,
410087, Oradea,
Romania
smbica@yahoo.com
abica@uoradea.ro

Abstract:

We present here a numerical method for first order delay ordinary differential equations, which use the Banach's fixed point theorem, the sequence of successive approximations and the trapezoidal quadrature rule. The error estimation of the method uses a recent result of P. Cerone and S.S. Dragomir about the remainder of the trapezoidal quadrature rule for Lipchitzian functions and for functions with continuous first derivative.

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Paper's Title:

Two Mappings Related to Steffensen's Inequalities

Author(s):

Liang-Cheng Wang

School of Mathematical Science,
Chongqing Institute of Technology,
Xingsheng Lu 4,
Yangjiaping 400050, Chongqing City,
China.
wangliangcheng@163.com

Abstract:

In this paper, we define two mappings closely connected with Steffensen's inequalities, investigate their main properties, give some refinements for Steffensen's inequalities and obtain new inequalities.

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Paper's Title:

Analysis of the Flow Field in Stenosed Bifurcated Arteries Through a Mathematical Model

Author(s):

S. Chakravarty and S. Sen

Department of Mathematics, Visva-Bharati University,
Santiniketan 731235,
India
santabrata2004@yahoo.co.in

Abstract:

The present study is dealt with an appropriate mathematical model of the arotic bifurcation in the presence of constrictions using which the physiological flow field is analized. The geometry of the bifurcated arterial segment having constrictions in both the parent and its daughter arterial lumen frequently occurring in the diseased arteries causing malfunction of the cardiovascular system , is formed mathematically with the introduction of appropriate curvatures at the lateral junctions and the flow divider. The flowing blood contained in the stenosed bifurcated artery is treated to be Newtonian and the flow is considered to be two dimensional. The motion of the arterial wall and its effect on local fluid mechanics is not ruled out from the present pursuit. The flow analysis applies the time-dependent, two-dimensional incompressible nonlinear Navier-Stokes equations for Newtonian fluid. The flow field can be obtained primarily following the radial coordinate transformation and using the appropriate boundary conditions and finally adopting a suitable finite difference scheme numerically. The influences of the arterial wall distensibility and the presence of stenosis on the flow field, the flow rate and the wall shear stresses are quantified in order to indicate the susceptibility to atherosclerotic lesions and thereby to validate the applicability of the present theoretical model.

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Paper's Title:

A Different Proof for the non-Existence of Hilbert-Schmidt Hankel Operators with Anti-Holomorphic Symbols on the Bergman Space

Author(s):

Georg Schneider

Universität Wien, Brünnerstr. 72 A-1210 Wien,
Austria.
georg.schneider@univie.ac.at
URL: http://www.univie.ac.at/bwl/cont/mitarbeiter/schneider.htm

Abstract:

We show that there are no (non-trivial) Hilbert-Schmidt Hankel operators with anti-holomorphic symbols on the Bergman space of the unit-ball B²(B^l) for l≥2. The result dates back to [6]. However, we give a different proof. The methodology can be easily applied to other more general settings. Especially, as indicated in the section containing generalizations, the new methodology allows to prove some robustness results for existing ones.

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Paper's Title:

Existence Results for Perturbed Fractional Differential Inclusions

Author(s):

Y.-K. Chang

Department of Mathematics,
Lanzhou Jiaotong University, Lanzhou, Gansu 730070, People's
Republic of China
lzchangyk@163.com

Abstract:

This paper is mainly concerned with the following fractional differential inclusions with boundary condition

A sufficient condition is established for the existence of solutions of the above problem by using a fixed point theorem for multivalued maps due to Dhage. Our result is proved under the mixed generalized Lipschitz and Carathéodory conditions.

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Paper's Title:

Inequalities for the Čebyšev Functional of Two Functions of Selfadjoint Operators in Hilbert Spaces

Author(s):

S. S. Dragomir

School of Engineering and Science
 Victoria University, PO 14428
 Melbourne City MC, Victoria 8001,
Australia
sever.dragomir@vu.edu.au
URL: http://www.staff.vu.edu.au/RGMIA/dragomir/

Abstract:

Some recent inequalities for the Čebyšev functional of two functions of selfadjoint linear operators in Hilbert spaces, under suitable assumptions for the involved functions and operators, are surveyed.

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Paper's Title:

Superquadracity, Bohr's Inequality and Deviation from a Mean Value

Author(s):

S. Abramovich, J. Barić, and J. Pečarić

Department of Mathematics, University of Haifa,
Haifa, 31905,
Israel
abramos@math.haifa.ac.il 

FESB, University of Split,
Rudera Bošcovića,
B.B., 21000, Split,
Croatia
jbaric@fesb.hr  

Faculty of Textile Technology, University of Zagreb,
Prilaz Baruna Filipovića,
30, 10000 Zagreb,
Croatia.
pecaric@hazu.hr  

Abstract:

Extensions of Bohr's inequality via superquadracity are obtained, where instead of the power p=2 which appears in Bohr's inequality we get similar results when we deal with p≥ 2 and with p≤ 2. Also, via superquadracity we extend a bound for deviation from a Mean Value.

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Paper's Title:

On the Sendov Conjecture for a Root Close to the Unit Circle

Author(s):

Indraneel G. Kasmalkar

Department of Mathematics,
University of California,
Berkeley, CA 94720
United States of America

E-mail: indraneelk@berkeley.edu 

Abstract:

On Sendov's conjecture, T. Chijiwa quantifies the idea stated by V. Vâjâitu and A. Zaharescu (and M. J. Miller independently), namely that if a polynomial with all roots inside the closed unit disk has a root sufficiently close to the unit circle then there is a critical point at a distance of at most one from that root. Chijiwa provides an estimate of exponential order for the required 'closeness' of the root to the unit circle so that such a critical point may exist. In this paper, we will improve this estimate to polynomial order by making major modifications and strengthening inequalities in Chijiwa's proof.

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Paper's Title:

To a Banach *-algebra in a Semipartial Dynamical System

Author(s):

Bahman Tabatabaie Shourijeh and Seyed Mostafa Zebarjad

Department of Mathematics,
College of Sciences,
Shiraz University, Shiraz 71454,
Iran.

E-mail: tabataba@math.susc.ac.ir    
zebarjad@mail.yu.ac.ir
URL: http://research.shirazu.ac.ir/faculty/More.asp?ID=207

Abstract:

By a partial dynamical system, we mean a triple containing a C*-algebra A, a discrete group G and a partial action of G on A. There are two C*--algebras associated to a given partial dynamical system. These are nothing but the certain C*-completions of a Banach *-algebra. In constructing such a Banach *-algebra, usually, a tedious limit process is used to apply. In this paper, we prove some theorems in this context without any limit process.

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Paper's Title:

Inequalities for the Area Balance of Functions of Bounded Variation

Author(s):

Sever S. Dragomir^1,2

¹Mathematics, School of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au

 
²DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL: http://rgmia.org/dragomir 

Abstract:

We introduce the area balance function associated to a Lebesgue integrable function f:[a,b] →C by

Several sharp bounds for functions of bounded variation are provided. Applications for Lipschitzian and convex functions are also given.

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Paper's Title:

Presentation a mathematical model for bone metastases control by using tamoxifen

Author(s):

Maryam Nikbakht, Alireza Fakharzadeh Jahromi and Aghileh Heydari

Department of Mathematics,
Payame Noor University,
P.O.Box 19395-3697, Tehran,
Iran.
.E-mail: maryam_nikbakht@pnu.ac.ir

Department of Mathematics,
Faculty of Basic Science,
Shiraz University of Technology.
E-mail: a_fakharzadeh@sutech.ac.ir

Department of Mathematics,
Payame Noor University,
P.O.Box 19395-3697, Tehran,
Iran.
E-mail: a-heidari@pnu.ac.ir

Abstract:

Bone is a common site for metastases (secondary tumor) because of breast and prostate cancer. According to our evaluations the mathematical aspect of the effect of drug in bone metastases has not been studied yet. Hence, this paper suggested a new mathematical model for bone metastases control by using tamoxifen. The proposed model is a system of nonlinear partial differential equations. In this paper our purpose is to present a control model for bone metastases. At end by some numerical simulations, the proposed model is examined by using physician.

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Paper's Title:

Stability Analysis Epidemic Model of SIR Type (Susceptible, Infectious, Recovered) On The Spread Dynamic of Malaria in Ambon City

Author(s):

Alwi Smith

Education Faculty, Biology Education Programme,
University of Pattimura,
Ir. M. Putuhena Street, Poka Ambon, Moluccas, 97233,
Indonesia.
E-mail:  alwi.smith1963@gmail.com

Abstract:

This research discusses the spread of malaria in Ambon city through SIR (Susceptible, Infected, Recovered) model. This research analyzes the stability of equilibrium point on deterministic model and Basic Reproduction Ratio (R₀). The result shows that the epidemic model has two equilibrium points. They are disease free equilibrium, [E₀=[S,I,R]=[1,0,0]], and epidemic equilibrium, E_i=[S,I,R]= [5,497808;-3,680341;-0,818288]. The Basic Reproduction Ratio of malaria disease in Ambon city is 0,181891. This result implies that malaria disease in Ambon will not be an endemic, because malaria disease in Ambon city will be eradicated slowly over time.

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12: Paper Source PDF document

Paper's Title:

Iterative Algorithm for Split Generalized Mixed Equilibrium Problem Involving Relaxed Monotone Mappings in Real Hilbert Spaces

Author(s):

¹U.A. Osisiogu, F.L. Adum, and ²C. Izuchukwu

¹Department of Mathematics and Computer Science,
Ebonyi State University, Abakaliki,
Nigeria.
E-mail: uosisiogu@gmail.com, adumson2@yahoo.com

²School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: izuchukwuc@ukzn.ac.za, izuchukwu_c@yahoo.com

Abstract:

The main purpose of this paper is to introduce a certain class of split generalized mixed equilibrium problem involving relaxed monotone mappings. To solve our proposed problem, we introduce an iterative algorithm and obtain its strong convergence to a solution of the split generalized mixed equilibrium problems in Hilbert spaces. As special cases of the proposed problem, we studied the proximal split feasibility problem and variational inclusion problem.

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Paper's Title:

The Concept of Convergence for 2-Dimensional Subspaces Sequence in Normed Spaces

Author(s):

M. Manuharawati, D. N. Yunianti, M. Jakfar

Mathematics Department, Universitas Negeri Surabaya,
Jalan Ketintang Gedung C8,
Surabaya 60321,
Indonesia.
E-mail: manuharawati@unesa.ac.id, dwiyunianti@unesa.ac.id,
muhammadjakfar@unesa.ac.id

Abstract:

In this paper, we present a concept of convergence of sequence, especially, of 2-dimensional subspaces of normed spaces. The properties of the concept are established. As consequences of our definition in an inner product space, we also obtain the continuity property of the angle between two 2-dimensional subspaces of inner product spaces.

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Paper's Title:

Inequalities of Gamma Function Appearing in Generalizing Probability Sampling Design

Author(s):

Mohammadkheer M. Al-Jararha And Jehad M. Al-Jararha

Department of Mathematics,
Yarmouk University,
Irbid 21163,
Jordan.
E-mail: mohammad.ja@yu.edu.jo

Department of Statistics,
Yarmouk University,
Irbid 21163,
Jordan.
E-mail: jehad@yu.edu.jo

Abstract:

In this paper, we investigate the complete monotonicity of some functions involving gamma function. Using the monotonic properties of these functions, we derived some inequalities involving gamma and beta functions. Such inequalities can be used to generalize different probability distribution functions. Also, they can be used to generalize some statistical designs, e.g., the probability proportional to the size without replacement design.

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Paper's Title:

ψ(m,q)-Isometric Mappings on Metric Spaces

Author(s):

Sid Ahmed Ould Beinane, Sidi Hamidou Jah and Sid Ahmed Ould Ahmed Mahmoud

Mathematical Analysis and Applications, Mathematics Department, College of Science,
Jouf University,
Sakaka P.O.Box 2014,
Saudi Arabia.
E-mail: beinane06@gmail.com

Department of Mathematics, College of Science Qassim University,
P.O. Box 6640, Buraydah 51452,
Saudi Arabia.
E-mail: jahsiidi@yahoo.fr

Mathematical Analysis and Applications,
Mathematics Department, College of Science, Jouf University,
Sakaka P.O.Box 2014,
Saudi Arabia.
E-mail: sidahmed@ju.edu.sa, sidahmed.sidha@gmail.com

Abstract:

The concept of (m,p)-isometric operators on Banach space was extended to (m,q)-isometric mappings on general metric spaces in [6]. This paper is devoted to define the concept of ψ(m, q)-isometric, which is the extension of A(m, p)-isometric operators on Banach spaces introduced in [10]. Let T,ψ: (E,d) -> (E, d) be two mappings.
For some positive integer m and q ∈ (0,∞). T is said to be an ψ(m,q)-isometry, if for all  y,z ∈ E,

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Paper's Title:

Sharp Inequalities Between Hölder and Stolarsky Means of Two Positive Numbers

Author(s):

M. Bustos Gonzalez and A. I. Stan

The University of Iowa,
Department of Mathematics,
14 MacLean Hall,
Iowa City, Iowa,
USA.
E-mail: margarita-bustosgonzalez@uiowa.edu
 
The Ohio State University at Marion,
Department of Mathematics,
1465 Mount Vernon Avenue,
Marion, Ohio,
USA.
E-mail: stan.7@osu.edu

Abstract:

Given any index of the Stolarsky means, we find the greatest and least indexes of the H\"older means, such that for any two positive numbers, the Stolarsky mean with the given index is bounded from below and above by the Hölder means with those indexes, of the two positive numbers. Finally, we present a geometric application of this inequality involving the Fermat-Torricelli point of a triangle.

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12: Paper Source PDF document

Paper's Title:

Using Direct and Fixed Point Technique of Cubic Functional Equation and its Hyers-Ulam Stability

Author(s):

Ramanuja Rao Kotti, Rajnesh Krishnan Mudaliar, Kaushal Neelam Devi, Shailendra Vikash Narayan

Fiji National University,
Department of Mathematics & Statistics,
P.O. Box 5529, Lautoka,
Fiji.
E-mail: ramanuja.kotti@fnu.ac.fj
URL: https://www.fnu.ac.fj

Abstract:

In this present work, we introduce a new type of finite dimensional cubic functional equation of the form

where Φ≥4 is an integer, and derive its general solution. The main purpose of this work is to investigate the Hyers-Ulam stability results for the above mentioned functional equation in Fuzzy Banach spaces by means of direct and fixed point methods.

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Paper's Title:

Meromorphic P-Valent Functions With Positive And Fixed Second Coefficients

Author(s):

B.A. Frasin and G. Murugusundaramoorthy

Department of Mathematics,
Al Al-Bayt University,
P.O. Box: 130095,
Mafraq, Jordan.
bafrasin@yahoo.com
URL: http://www.geocities.com/bafrasin/techie.html

Department of Mathematics,
Vellore Institute of Technology,
Deemed University,
Vellore - 632014,
India.
gmsmoorthy@yahoo.com

Abstract:

We introduce the classes and of meromorphic univalent functions ith positive and fixed second coefficients. The aim of the present paper is to obtain coefficient inequalities and closure theorems for these classes. Furthermore, the radii of convexity and starlikeness for functions the classes and are determined.

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Paper's Title:

Some Stability Results For Fixed Point Iteration Processes

Author(s):

M. O. Olatinwo, O. O. Owojori, and C. O. Imoru

Department of Mathematics, Obafemi Awolowo University,
Ile-Ife,
Nigeria.
polatinwo@oauife.edu.ng
walejori@oauife.edu.ng
cimoru@oauife.edu.ng

Abstract:

In this paper, we present some stability results for both the general Krasnoselskij and the Kirk's iteration processes. The method of Berinde \cite{VBE1} is employed but a more general contractive condition than those of Berinde \cite{VBE1}, Harder and Hicks \cite{HAM}, Rhoades \cite{RHO1} and Osilike \cite{OSI1} is considered.

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11: Paper Source PDF document

Paper's Title:

Coincidences and Fixed Points of Hybrid Maps in Symmetric Spaces

Author(s):

S. L. Singh and Bhagwati Prasad

Vedic MRI, 21 Govind Nagar,
Rishikesh 249201
India
vedicmri@gmail.com

Department of Mathematics, Gurukula Kangri University,
Hardwar 249404,
India

Abstract:

The purpose of this paper is to obtain a new coincidence theorem for a single-valued and two multivalued operators in symmetric spaces. We derive fixed point theorems and discuss some special cases and applications.

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11: Paper Source PDF document

Paper's Title:

Numerical Studies on Dynamical Systems Method for Solving Ill-posed Problems with Noise

Author(s):

N. H. Sweilam and A. M. Nagy

Mathematics Department, Faculty of Science,
Cairo University,
Giza, Egypt.
n_sweilam@yahoo.com

Mathematics Department, Faculty of Science,
Benha University,
Benha, Egypt.
abdelhameed_nagy@yahoo.com

Abstract:

In this paper, we apply the dynamical systems method proposed by A. G. RAMM, and the the variational regularization method to obtain numerical solution to some ill-posed problems with noise. The results obtained are compared to exact solutions. It is found that the dynamical systems method is preferable because it is easier to apply, highly stable, robust, and it always converges to the solution even for large size models.

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11: Paper Source PDF document

Paper's Title:

On the Numerical Solution for Deconvolution Problems with Noise

Author(s):

N. H. Sweilam

Cairo University, Faculty of Science, Mathematics Department,
Giza, Egypt.
n-sweilam@yahoo.com

Abstract:

In this paper three different stable methods for solving numerically deconvolution problems with noise are studied. The methods examined are the variational regularization method, the dynamical systems method, and the iterative regularized processes. Gravity surveying problem with noise is studied as a model problem. The results obtained by these methods are compared to the exact solution for the model problem. It is found that these three methods are highly stable methods and always converge to the solution even for large size models. The relative higher accuracy is obtained by using the iterative regularized processes.

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11: Paper Source PDF document

Paper's Title:

On Pseudo Almost Periodic Solutions to Some Neutral Functional-Differential Equations

Author(s):

Toka Diagana and Eduardo Hernández

Department of Mathematics, Howard University
2441 6th Street NW, Washington DC 20059,
USA.
tdiagana@howard.edu

Departamento de Matemática, I.C.M.C. Universidade de São Paulo,
Caixa Postal 668, 13560-970, São Carlos SP,
Brazil.
lalohm@icmc.sc.usp.br

Abstract:

This paper discusses the existence and uniqueness of pseudo almost periodic solutions to a class of partial neutral functional-differential equations. Under some suitable assumptions, existence and uniqueness results are obtained. An example is given to illustrate abstract results.

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Paper's Title:

Existence of Large Solutions to Non-Monotone Semilinear Elliptic Equations

Author(s):

Alan V. Lair, Zachary J. Proano, and Aihua W. Wood

Air Force Institute of Technology
2950 Hobson Way, AFIT/ENC
Wright-Patterson Air Force Base, OH, 45433-7765,
USA.
Aihua.Wood@afit.edu
URL: www.afit.edu

Abstract:

We study the existence of large solutions of the semilinear elliptic equation Δu=p(x)f(u) where f is not monotonic. We prove existence, on bounded and unbounded domains, under the assumption that f is Lipschitz continuous, f(0) = 0, f(s) > 0 for s > 0 and there exists a nonnegative, nondecreasing Hölder continuous function g and a constant M such that g(s) ≤ f(s) ≤ Mg(s) for large s. The nonnegative function p is allowed to be zero on much of the domain.

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Paper's Title:

On Stable Numerical Differentiation

Author(s):

N. S. Hoang and A. G. Ramm

Mathematics Department, Kansas State University
Manhattan, KS 66506-2602,
U. S. A.
nguyenhs@math.ksu.edu
ramm@math.ksu.edu
URL:http://math.ksu.edu/~ramm

Abstract:

Based on a regularized Volterra equation, two different approaches for numerical differentiation are considered. The first approach consists of solving a regularized Volterra equation while the second approach is based on solving a disretized version of the regularized Volterra equation. Numerical experiments show that these methods are efficient and compete favorably with the variational regularization method for stable calculating the derivatives of noisy functions.

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Paper's Title:

Ulam Stability of Reciprocal Difference and Adjoint Functional Equations

Author(s):

K. Ravi, J. M. Rassias and B. V. Senthil Kumar

Department of Mathematics,
Sacred Heart College, Tirupattur - 635601,
India

Pedagogical Department E. E.,
Section of Mathematics and Informatics,
National and Capodistrian University of Athens,
4, Agamemnonos Str., Aghia Paraskevi,
Athens, Attikis 15342,
GREECE

Department of Mathematics,
C.Abdul Hakeem College of Engineering and
Technology, Melvisharam - 632 509, India

shckavi@yahoo.co.in
jrassias@primedu.uoa.gr
bvssree@yahoo.co.in
 

Abstract:

In this paper, the reciprocal difference functional equation (or RDF equation) and the reciprocal adjoint functional equation (or RAF equation) are introduced. Then the pertinent Ulam stability problem for these functional equations is solved, together with the extended Ulam (or Rassias) stability problem and the generalized Ulam (or Ulam-Gavruta-Rassias) stability problem for the same equations.

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Paper's Title:

Growth and Products of Subharmonic Functions in the Unit Ball

Author(s):

R. Supper

Université de Strasbourg,
UFR de Mathématique et Informatique, URA CNRS 001,
7 rue René Descartes,
F--67 084 Strasbourg Cedex,
France
raphaele.supper@math.unistra.fr

Abstract:

The purpose of this paper is to link information on the application u→gu with some growth conditions on the functions u and g subharmonic in the unit ball of R^N. Two kinds of growth are considered: the Bloch--type growth and growth conditions expressed through integrals involving involutions of the unit ball.

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Paper's Title:

On A Conjecture of A Logarithmically Completely Monotonic Function

Author(s):

Valmir Krasniqi, Armend Sh. Shabani

Department of Mathematics,
University of Prishtina,
Republic of Kosova

E-mail: vali.99@hotmail.com  
armend_shabani@hotmail.com

Abstract:

In this short note we prove a conjecture, related to a logarithmically completely monotonic function, presented in [5]. Then, we extend by proving a more generalized theorem. At the end we pose an open problem on a logarithmically completely monotonic function involving q-Digamma function.

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Paper's Title:

A Dynamic Contact Problem for an Electro Viscoelastic Body

Author(s):

Denche M. and Ait Kaki L.

Laboratoire Equations Differentielles,
Departement de Mathematiques,
Universite Constantine 1,
Algeria.

Ecole Normale Superieure,
Departement des Sciences Exactes et Informatique,
Plateau Mansourah, Constantine.
Algeria.

E-mail: m.denche@umc.edu.dz
leilaitkaki@yahoo.fr

Abstract:

We consider a dynamic problem which describes a contact between a piezoelectric body and a conductive foundation. The frictionless contact is modelled with the normal compliance, the electric conditions are supposed almost perfect. We prove the existence of a unique weak solution for almost perfect electric contact.

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Paper's Title:

On operators for which T²≥-T^*2

Author(s):

Messaoud Guesba¹ and Mostefa Nadir²

¹Department of Mathematics,
University of El Oued 39000,
Algeria
E-mail: guesbamessaoud2@gmail.com

 
²Department of Mathematics,
University of Msila 28000,
Algeria
E-mail: mostefanadir@yahoo.fr

Abstract:

In this paper we introduce the new class of operators for which T²≥ -T^*2 acting on a complex Hilbert space H. We give some basic properties of these operators. we study the relation between the class and some other well known classes of operators acting on H.

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Paper's Title:

Characterization of Caristi Type Mapping Through its Absolute Derivative

Author(s):

M. Muslikh¹, A. Kilicman^2,3, S. H. Sapar⁴ and N. Bacho⁵

¹Department of Mathematics,
University of Brawijaya,
Malang 65143, East Java,
Indonesia.
E-mail: mslk@ub.ac.id

²Department of Mathematics,
Universiti Putra Malaysia,
43400 UPM, Serdang, Selangor,
Malaysia
E-mail: akilic@upm.edu.my

³Department of Electrical and Electronic Engineering,
Istanbul Gelisim University,
Avcilar, Istanbul,
Turkey

⁴Department of Mathematics,
Universiti Putra Malaysia,
43400 UPM, Serdang, Selangor,
Malaysia
E-mail: sitihas@upm.edu.my

⁵Department of Mathematics,
Universiti Putra Malaysia,
43400 UPM, Serdang, Selangor,
Malaysia
E-mail: norfifah@upm.edu.my

Abstract:

The purpose of this article to characterize the Caristi type mapping by the absolute derivative. The equivalences of the Caristi mapping with contraction mapping is discussed too. In addition, it was shown that the contraction mapping can be tested through its absolute derivative.

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Paper's Title:

A New Interpretation of the Number e

Author(s):

Olivier de La Grandville

Faculty of Economics, Goethe University,
Frankfurt, Theodor-Adorno Platz 4,
60323 Frankfurt am Main,
Germany.
E-mail: odelagrandville@gmail.com

Abstract:

We show that e is the amount that 1 becomes when it is invested during an arbitrary time span of length T, at any continuously compounded interest rates as long as their average is equal to 1/T . A purely mathematical interpretation of e is the amount a unit quantity becomes after any duration T when the average of its instantaneous growth rates is 1/T. This property can be shown to remain valid if T tends to infinity as long as the integral of the growth rates converges to unity.

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Paper's Title:

Analysis of a Dynamic Elasto-viscoplastic Frictionless Antiplan Contact Problem with Normal Compliance

Author(s):

A. Ourahmoun¹, B. Bouderah², T. Serrar³

^1,2Applied Mathematics Laboratory,
M'sila University, 28000,
Algeria.
E-mail: ourahmounabbes@yahoo.fr

³Applied Mathematics Laboratory,
Setif 1 University, 19000,
Algeria.

Abstract:

We consider a mathematical model which describes the dynamic evolution of a thermo elasto viscoplastic contact problem between a body and a rigid foundation. The mechanical and thermal properties of the obstacle coating material near its surface. A variational formulation of this dynamic contact phenomenon is derived in the context of general models of thermo elasto viscoplastic materials. The displacements and temperatures of the bodies in contact are governed by the coupled system consisting of a variational inequality and a parabolic differential equation. The proof is based on a classical existence and uniqueness result on parabolic inequalities,differential equations and fixed point arguments.

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Paper's Title:

On Admissible Mapping via Simulation Function

Author(s):

Anantachai Padcharoen and Pakeeta Sukprasert

Department of Mathematics,
Faculty of Science and Technology,
Rambhai Barni Rajabhat University,
Chanthaburi 22000,
Thailand.
E-mail: anantachai.p@rbru.ac.th
 
Department of Mathematics and Computer Science
Faculty of Science and Technology
Rajamangala University of Technology Thanyaburi (RMUTT),
Thanyaburi, Pathumthani 12110,
Thailand.
E-mail: pakeeta_s@rmutt.ac.th

Abstract:

In this paper, we present some fixed point results in complete metric spaces by using generalized admissible mapping embedded in the simulation function. Its applications, Our results used to study the existence problem of nonlinear Hammerstein integral equations.

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Paper's Title:

Some Remarks On Quasinearly Subharmonic Functions

Author(s):

Mansour Kalantar

Universite Toulouse III-Paul Sabatier,
118 Route de Narbonne, 31062 Toulouse,
France.
E-mail: mansour.kalantar@math.univ-toulouse.fr, mankalantar12@yahoo.com

Abstract:

We prove some basic properties of quasi-nearly subharmonic functions and quasi-nearly subharmonic functions in the narrow sense.

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Paper's Title:

A Caratheodory's Approximate Solutions of Stochastic Differential Equations Under the Hölder Condition

Author(s):

Bo-Kyeong Kim and Young-Ho Kim

Department of Mathematics,
Changwon National University,
Changwon, Gyeongsangnam-do 51140,
Korea.
E-mail: claire9576@naver.com
yhkim@changwon.ac.kr

Abstract:

In this paper, based on the theorem of the uniqueness of the solution of the stochastic differential equation, the convergence possibility of the Caratheodory's approximate solution was studied by approximating the unique solution. To obtain this convergence theorem, we used a Hölder condition and a weakened linear growth condition. Furthermore, The auxiliary theorems for the existence and continuity of the Caratheodory's approximate solution were investigated as a prerequisite.

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Paper's Title:

Introducing the Picard-S3 Iteration for Fixed Points

Author(s):

Pravin Singh, Virath Singh and Shivani Singh

University of KwaZulu-Natal,
School of Mathematics Statistics and Computer Sciences,
Private Bag X54001,
Durban, 4000
South Africa.

Unisa,
Department of Decision Sciences,
PO Box 392,
Pretoria, 0003
South Africa.
E-mail: singhprook@gmail.com
singhv@ukzn.ac.za
shivstarsingh@gmail.com

Abstract:

In this paper we introduce a three step iteration method and show that it can be used to approximate the fixed point of a weak contraction mapping. Furthermore, we prove that this scheme is equivalent to the Mann iterative scheme. A comparison is made with other three step iterative methods by examining the speed of convergence. Results are presented in tables to support our conclusion.

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Paper's Title:

Constraint Qualifications for Multiobjective Programming Problems on Hadamard Manifolds

Author(s):

Arnav Ghosh, Balendu Bhooshan Upadhyay and I.M. Stancu-Minasian

Department of Mathematics,
Indian Institute of Technology Patna,
Patna,
India.
E-mail: arnav_2021ma09@iitp.ac.in

Department of Mathematics,
Indian Institute of Technology Patna,
Patna,
India.
E-mail: bhooshan@iitp.ac.in

"Gheorghe Mihoc-Caius Iacob" Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy,
Bucharest,
Romania.
E-mail: stancu_minasian@yahoo.com 

Abstract:

The study of optimization methods on manifolds has emerged as an immensely significant topic in mathematics due its ubiquitous applicability as well as various computational advantages associated with it. Motivated by this fact, the present article is devoted to the study of a class of constrained multiobjective programming problems (MOPP) in the framework of Hadamard manifolds. We present the generalized Guignard constraint qualification (GGCQ) in the framework of Hadamard manifolds for (MOPP). Employing (GGCQ), we derive Karush-Kuhn-Tucker type necessary optimality criteria for (MOPP). Moreover, we present several other constraint qualifications (CQs) on Hadamard manifolds, namely, Abadie's CQ, generalized Abadie's CQ, Cottle-type CQ, Slater-type CQ, linear CQ, linear objective CQ and Mangasarian-Fromovitz CQ. Further, we establish various relations between these constraint qualifications. In particular, we show that these constraint qualifications, in turn, become sufficient conditions ensuring that (GGCQ) is satisfied.

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Paper's Title:

Solving Fixed Point Problems and Variational Inclusions Using Viscosity Approximations

Author(s):

P. Patel, R. Shukla

Department of Mathematics, School of Advanced Sciences, VIT-AP University\\
Amaravati, 522237, Andhra Pradesh,
India.
E-mail: prashant.patel9999@gmail.com, prashant.p@vitap.ac.in

Department of Mathematical Sciences & Computing, Walter Sisulu University,
Mthatha 5117,
South Africa.
E-mail: rshukla@wsu.ac.za

Abstract:

This paper proposes a new algorithm to find a common element of the fixed point set of a finite family of demimetric mappings and the set of solutions of a general split variational inclusion problem in Hilbert spaces. The algorithm is based on the viscosity approximation method, which is a powerful tool for solving fixed point problems and variational inclusion problems. Under some conditions, we prove that the sequence generated by the algorithm converges strongly to this common solution.

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Paper's Title:

Compactly Supported Interpolatory Orthogonal Multiwavelet Packets

Author(s):

Yang Shouzhi

Department of Mathematics,
Shantou University,
Shantou, Po Box 515063,
P.R.China.
szyang@stu.edu.cn

 

Abstract:

Compactly supported interpolatory orthogonal multiwavelet packets are introduced. Precisely, if both the multiscaling function and the corresponding multiwavelet have the same interpolatory property, then the multiwavelet packets are also interpolatory orthogonal. Thus, the coefficients of decomposition or synthesis of multiwavelet packets can be realized by sampling instead of inner products. This multiwavelet packets provide a finer decomposition of multiwavelet packets space and give a better localization.

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Paper's Title:

On Vector Variational Inequality Problem in Terms of Bifunctions

Author(s):

C. S. Lalitha and Monika Mehta

Department of Mathematics, Rajdhani College,
University of Delhi, Raja Garden,
Delhi 110015, India
cslalitha@rediffmail.com

Department of Mathematics, Satyawati College,
University Of Delhi, Ashok Vihar,
Phase-III, Delhi 110052, India
mridul_in@yahoo.com

Abstract:

In this paper, we consider a generalized vector variational inequality problem expressed in terms of a bifunction and establish existence theorems for this problem by using the concepts of cone convexity and cone strong quasiconvexity and employing the celebrated Fan's Lemma. We also give two types of gap functions for this problem.

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Paper's Title:

A Wallis Type Inequality and a Double Inequality for Probability Integral

Author(s):

Jian Cao, Da-Wei Niu and Feng Qi

School of Mathematics and Informatics,
Henan Polytechnic University, Jiaozuo City,
Henan Province, 454010,
China
21caojian@163.com

School of Mathematics and Informatics,
Henan Polytechnic University, Jiaozuo City,
Henan Province, 454010,
China
nnddww@tom.com

Research Institute of Mathematical Inequality Theory,
Henan Polytechnic University, Jiaozuo City,
Henan Province, 454010,
China
qifeng@hpu.edu.cn
fengqi618@member.ams.org
qifeng618@hotmail.com
qifeng618@msn.com
qifeng618@qq.com
URL: http://rgmia.vu.edu.au/qi.html

Abstract:

In this short note, a Wallis type inequality with the best upper and lower bounds is established. As an application, a double inequality for the probability integral is found.

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Paper's Title:

The Iterated Variational Method for the Eigenelements of a Class of Two-Point Boundary Value Problems

Author(s):

Muhammed I. Syam and Qasem M. Al-Mdallal

Department of Mathematical Sciences, College of Science, UAE University,
P. O. Box 17551, Al-Ain,
United Arab Emirates
Q.Almdallal@uaeu.ac.ae
M.Syam@uaeu.ac.ae

Abstract:

The iterated variational method is considered in the approximation of eigenvalues and eigenfunctions for a class of two point boundary value problems. The implementation of this method is easy and competes well with other methods. Numerical examples are presented to show the efficiency of the method proposed. Comparison with the work of others is also illustrated.

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Paper's Title:

An Approximation of Jordan Decomposable Functions for a Lipschitz Function

Author(s):

Ibraheem Alolyan

Mathematics Department,
College of Science, King Saud University
P.O.Box: 2455, Riyadh 11451,
Saudi Arabia
ialolyan05@yahoo.com

Abstract:

The well known Jordan decomposition theorem gives the useful characterization that any function of bounded variation can be written as the difference of two increasing functions. Functions which can be expressed in this way can be used to formulate an exclusion test for the recent Cellular Exclusion Algorithms for numerically computing all zero points or the global minima of functions in a given cellular domain [2,8,9]. In this paper we give an algorithm to approximate such increasing functions when only the values of the function of bounded variation can be computed. For this purpose, we are led to introduce the idea of ε-increasing functions. It is shown that for any Lipschitz continuous function, we can find two ε-increasing functions such that the Lipschitz function can be written as the difference of these functions.

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Paper's Title:

Contact With Adhesion between a Deformable Body and a Foundation

Author(s):

B. Teniou and M. Sofonea

Laboratoire de Mathematiques Appliquées et Modélisation,
Université Mentouri, Constantine 25000,
Algeria
tenioubou2@yahoo.fr

Laboratoire de Mathématiques et Physiques pour les Systémes,
Univesité de Perpignan,
France.
sofonea@univ-perp.fr
 

Abstract:

The aim of this work is study a dynamic contact problem between a deformable body and a foundation where the deformations are supposed to be small. The contact is with adhesion and normal compliance. The behavior of this body is modeled by a nonlinear elastic-visco-plastic law. The evolution of bonding field is described by a nonlinear differential equation. We derive a variational formulation of the contact problem and we prove the existence and uniqueness of its solution. The proof is based on the construction of three intermediate problems and then we construct a contraction mapping whose unique fixed point will be the weak solution of the mechanical problem.

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Paper's Title:

An Improved Mesh Independence Principle for Solving Equations and their Discretizations using Newton's Method

Author(s):

Ioannis K. Argyros

Cameron university,
Department of Mathematics Sciences,
Lawton, OK 73505,
USA
iargyros@cameron.edu  

Abstract:

We improve the mesh independence principle [1] which states that when Newton's method is applied to an equation on a Banach space as well as to their finite--dimensional discretization there is a difference of at most one between the number of steps required by the two processes to converge to within a given error tolerance. Here using a combination of Lipschitz and center Lipschitz continuity assumptions instead of just Lipschitz conditions we show that the minimum number of steps required can be at least as small as in earlier works. Some numerical examples are provided whereas our results compare favorably with earlier ones.

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Paper's Title:

Inclusion and Neighborhood Properties for Certain Subclasses of Analytic Functions Associated with Convolution Structure

Author(s):

M. K. Aouf

Mathematics Department,
Faculty of Science,
Mansoura University 35516,
Egypt.
mkaouf127@yahoo.com

Abstract:

In this paper we introduce and investigate two new subclasses of multivalently analytic functions of complex order defined by using the familiar convolution structure of analytic functions. In this paper we obtain the coefficient estimates and the consequent inclusion relationships involving the neighborhoods of the p-valently analytic functions.

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Paper's Title:

Some Homogeneous Cyclic Inequalities of Three Variables of Degree Three and Four

Author(s):

TETSUYA ANDO

Department of Mathematics and Informatics,
 Chiba University, Chiba 263-8522, JAPAN

ando@math.s.chiba-u.ac.jp

Abstract:

We shall show that the three variable cubic inequality
    t² (a³+b³+c³) + (t⁴-2t)(ab²+bc²+ca²)
            ≥ (2t³-1)(a²b+b²c+c²a) + (3t⁴-6t³+3t²-6t+3)abc
holds for non-negative a, b, c, and for any real number t.
We also show some similar three variable cyclic quartic inequalities.
 

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Paper's Title:

Further Bounds for Two Mappings Related to the Hermite-Hadamard Inequality

Author(s):

S. S. Dragomir^1,2 and I. Gomm¹

¹Mathematics, School of Engineering & Science,
Victoria University,
PO Box 14428, Melbourne City, MC 8001,
Australia.

²School of Computational & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa.

sever.dragomir@vu.edu.au
ian.gomm@vu.edu.au
URL: http://rgmia.org/dragomir  
 

Abstract:

Some new results concerning two mappings associated to the celebrated Hermite-Hadamard integral inequality for twice differentiable functions with applications for special means are given.

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Paper's Title:

A Geometric Generalization of Busemann-Petty Problem

Author(s):

Liu Rong and Yuan Jun

Shanghai Zhangjiang Group Junior Middle School,
Huo Xiang Road, Shanghai, 201203,
China

yuanjun_math@126.com

liurong@shu.edu.cn

Abstract:

The norm defined by Busemann's inequality establishes a class of star body - intersection body. This class of star body plays a key role in the solution of Busemann-Petty problem. In 2003, Giannapoulos [1] defined a norm for a new class of half-section. Based on this norm, we give a geometric generalization of Busemann-Petty problem, and get its answer as a result

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Paper's Title:

Schwarz Method for Variational Inequalities Related to Ergodic Control Problems

Author(s):

S. Saadi, H. Mécheri

Department of Mathematics, Badji Mokhtar University, Annaba 23000,
P.O.Box. 12, Annaba 23000, Algeria

signor_2000@yahoo.fr

Mcherihalima@yahoo.fr

Abstract:

In this paper, we study variational inequalities related to ergodic control problems studied by M. Boulbrachène and H. Sissaoui [11], where the "discount factor" (i.e., the zero order term) is set to 0, we use an overlapping Schwarz method on nomatching grid which consists in decomposing the domain in two subdomains. For α ∈ ]0.1[ we provide the discretization on each subdomain converges in L^∞ -norm.

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Paper's Title:

Relation Between The Set Of Non-decreasing Functions And The Set Of Convex Functions

Author(s):

Qefsere Doko Gjonbalaj and Luigj Gjoka

Department of Mathematics, Faculty of Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000,
Kosova

E-mail: qefsere.gjonbalaj@uni-pr.edu
 

Department of Engineering Mathematics,
Polytechnic University of Tirana, Tirana,
Albania.

E-mail: luigjgjoka@ymail.com

Abstract:

In this article we address the problem of integral presentation of a convex function. Let I be an interval in R. Here, using the Riemann or Lebesgue’s integration theory, we find the necessary and sufficient condition for a function f: I→ R to be convex in I.

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Paper's Title:

The Functional Equation With an Exponential Polynomial Solution and its Stability

Author(s):

Young Whan Lee¹, Gwang Hui Kim^2*, and Jeong Il Kim³

¹Department of Computer Hacking and Information Security,
College of Engineering, Daejeon University,
Daejeon, 34520,
Korea(Republic of).
E-mail: ywlee@dju.ac.kr

²Department of Mathematics,
Kangnam University,
Yongin, Gyeonggi, 16979,
Korea(Republic of).
E-mail: ighkim@kangnam.ac.kr

³Department of Statistics,
Daejeon University,
Daejeon 34520,
Korea(Republic of).
E-mail: jlkim@dju.ac.kr

Abstract:

In this paper, we prove that the unique continuous solution of the functional equation

is

where p_n(x) is a polynomial with degree n and

We also obtain the superstability and stability of the functional equation with the following forms, respectively:

 

and

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Paper's Title:

Some Inequalities of the Hermite-Hadamard Type for k-Fractional Conformable Integrals

Author(s):

C.-J. Huang, G. Rahman, K. S. Nisar, A. Ghaffar and F. Qi

Department of Mathematics, Ganzhou Teachers College,
Ganzhou 341000, Jiangxi,
China.
E-mail: hcj73jx@126.com , huangcj1973@qq.com

Department of Mathematics, Shaheed Benazir Bhutto University,
Sheringal, Upper Dir, Khyber Pakhtoonkhwa,
Pakistan.
E-mail: gauhar55uom@gmail.com

Department of Mathematics, College of Arts and Science at Wadi Aldawaser, 11991,
Prince Sattam Bin Abdulaziz University, Riyadh Region,
Kingdom of Saudi Arabia.
E-mail: n.sooppy@psau.edu.sa, ksnisar1@gmail.com

Department of Mathematical Science, Balochistan University of Information Technology,
Engineering and Management Sciences, Quetta,
Pakistan.
E-mail: abdulghaffar.jaffar@gmail.com

School of Mathematical Sciences, Tianjin Polytechnic University,
Tianjin 300387,
China; Institute of Mathematics,
Henan Polytechnic University, Jiaozuo 454010, Henan,
China.
E-mail: qifeng618@gmail.com, qifeng618@qq.com

 

Abstract:

In the paper, the authors deal with generalized k-fractional conformable integrals, establish some inequalities of the Hermite-Hadamard type for generalized k-fractional conformable integrals for convex functions, and generalize known inequalities of the Hermite-Hadamard type for conformable fractional integrals.

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Paper's Title:

Generalised Models for Torsional Spine Reconnection

Author(s):

Ali Khalaf Hussain Al-Hachami

Department of Mathematics,
College of Education For Pure Sciences,
Wasit University,
Iraq.
E-mail: alhachamia@uowasit.edu.iq

Abstract:

Three-dimensional (3D) null points are available in wealth in the solar corona, and the equivalent is probably going to be valid in other astrophysical situations. On-going outcomes from sun oriented perceptions and from reproductions propose that reconnection at such 3D nulls may assume a significant job in the coronal dynamics. The properties of the torsional spine method of magnetic reconnection at 3D nulls are researched. Kinematic model are created, which incorporate the term ηJ that is spatially localised around the null, stretching out along the spine of the null. The null point is to research the impact of shifting the level of asymmetry of the null point magnetic field on the subsequent reconnection process where past examinations constantly considered a non-nonexclusive radially symmetric null. Specifically we analyse the rate of reconnection of magnetic flux at the spine of null point. Logical arrangements are determined for the enduring kinematic equation, and contrasted and the after effects of torsional spine reconnection models when the current is restricted in which the Maxwell conditions are illuminated. The geometry of the current layers inside which torsional spine reconnection happen is autonomous on the symmetry of the magnetic field. Torsional spine reconnection happens in a thin cylinder around the spine, with circular cross-segment when the fan eigenvalues are extraordinary. The short axis of the circle being along the solid field bearing. Just as it was discovered that the fundamental structure of the method of attractive reconnection considered is unaffected by changing the magnetic field symmetry, that is, the plasma flow is discovered rotational around the spine of null point. The spatiotemporal pinnacle current, and the pinnacle reconnection rate achieved, are found not to rely upon the level of asymmetry.

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Paper's Title:

Accuracy of Implicit DIMSIMs with Extrapolation

Author(s):

A. J. Kadhim, A. Gorgey, N. Arbin and N. Razali

Mathematics Department, Faculty of Science and Mathematics,
Sultan Idris Education University,
35900 Tanjong Malim, Perak,
Malaysia
E-mail: annie_gorgey@fsmt.upsi.edu.my

Unit of Fundamental Engineering Studies,
Faculty of Engineering, Built Environment,
The National University of Malaysia,
43600 Bangi,
Malaysia.

Abstract:

The main aim of this article is to present recent results concerning diagonal implicit multistage integration methods (DIMSIMs) with extrapolation in solving stiff problems. Implicit methods with extrapolation have been proven to be very useful in solving problems with stiff components. There are many articles written on extrapolation of Runge-Kutta methods however fewer articles on extrapolation were written for general linear methods. Passive extrapolation is more stable than active extrapolation as proven in many literature when solving stiff problems by the Runge-Kutta methods. This article takes the first step by investigating the performance of passive extrapolation for DIMSIMs type-2 methods. In the variable stepsize and order codes, order-2 and order-3 DIMSIMs with extrapolation are investigated for Van der Pol and HIRES problems. Comparisons are made with ode23 solver and the numerical experiments showed that implicit DIMSIMs with extrapolation has greater accuracy than the method itself without extrapolation and ode23.

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Paper's Title:

Numerical Approximation by the Method of Lines with Finite-volume Approach of a Solute Transport Equation in Periodic Heterogeneous Porous Medium

Author(s):

D. J. Bambi Pemba and B. Ondami

Université Marien Ngouabi,
Factuté des Sciences et Techniques,
BP 69, Brazzaville,
Congo.
E-mail: bondami@gmail.com

Abstract:

In this paper we are interested in the numerical approximation of a two-dimensional solute transport equation in heterogeneous porous media having periodic structures. It is a class of problems which has been the subject of various works in the literature, where different methods are proposed for the determination of the so-called homogenized problem. We are interested in this paper, in the direct resolution of the problem, and we use the method of lines with a finite volume approach to discretize this equation. This discretization leads to an ordinary differential equation (ODE) that we discretize by the Euler implicit scheme. Numerical experiments comparing the obtained solution and the homogenized problem solution are presented. They show that the precision and robustness of this method depend on the ratio between, the mesh size and the parameter involved in the periodic homogenization.

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Paper's Title:

Solving Non-Autonomous Nonlinear Systems of Ordinary Differential Equations Using Multi-Stage Differential Transform Method

Author(s):

K. A. Ahmad, Z. Zainuddin, F. A. Abdullah

School of Mathematical Sciences Universiti Sains Malaysia
11800 USM Penang
Malaysia.
E-mail: abumohmmadkh@hotmail.com
zarita@usm.my
farahaini@usm.my

Abstract:

Differential equations are basic tools to describe a wide variety of phenomena in nature such as, electrostatics, physics, chemistry, economics, etc. In this paper, a technique is developed to solve nonlinear and linear systems of ordinary differential equations based on the standard Differential Transform Method (DTM) and Multi-stage Differential Transform Method (MsDTM). Comparative numerical results that we are obtained by MsDTM and Runge-Kutta method are proposed. The numerical results showed that the MsDTM gives more accurate approximation as compared to the Runge-Kutta numerical method for the solutions of nonlinear and linear systems of ordinary differential equations

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Paper's Title:

Antiderivatives and Integrals Involving Incomplete Beta Functions with Applications

Author(s):

R. AlAhmad^1,2 and H. Almefleh¹

Mathematics Department,
Yarmouk University,
Irbid 21163,
Jordan.
E-mail: rami_thenat@yu.edu.jo

Faculty of Engineering,
Higher Colleges of Technology,
Ras Alkhaimah,
UAE.

Abstract:

In this paper, we prove that incomplete beta functions are antiderivatives of several products and powers of trigonometric functions, we give formulas for antiderivatives for products and powers of trigonometric functions in term of incomplete beta functions, and we evaluate integrals involving trigonometric functions using incomplete beta functions. Also, we extend some properties of the beta functions to the incomplete beta functions. As an application for the above results, we find the moments for certain probability distributions.

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Paper's Title:

A New Relaxed b-metric Type and Fixed Point Results

Author(s):

P. Singh, V. Singh and Thokozani Cyprian Martin Jele

Department of Mathematics,
University of KwaZulu-Natal,
Private Bag X54001, Durban,
South Africa.
E-mail: singhp@ukzn.ac.za, singhv@ukzn.ac.za, thokozani.jele@nwu.ac.za

Abstract:

The purpose of this paper is to introduce a new relaxed α, β b-metric type by relaxing the triangle inequality. We investigate the effect that this generalization has on fixed point theorems.

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Paper's Title:

Numerical Solution of Certain Types of Fredholm-Volterra Integro-Fractional Differential Equations via Bernstein Polynomials

Author(s):

Alias B. Khalaf¹, Azhaar H. Sallo² and Shazad S. Ahmed³

¹Department of Mathematics, College of Science,
University of Duhok,
Kurdistan Region,
Iraq.
E-mail:  aliasbkhalaf@uod.ac

²Department of Mathematics, College of Science,
University of Duhok,
Kurdistan Region,
Iraq.
E-mail:  azhaarsallo@uod.ac

³Department of Mathematics, College of Science,
University of Sulaimani,
Kurdistan Region,
Iraq.
E-mail: shazad.ahmed@univsul.edu

 

Abstract:

In this article we obtain a numerical solution for a certain fractional order integro-differential equations of Fredholm-Volterra type, where the fractional derivative is defined in Caputo sense. The properties of Bernstein polynomials are applied in order to convert the fractional order integro-differential equations to the solution of algebraic equations. Some numerical examples are investigated to illustrate the method. Moreover, the results obtained by this method are compared with the exact solution and with the results of some existing methods as well.

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Paper's Title:

Lozi Maps With Max Function and its Application

Author(s):

Abdellah Menasri

Higher National School of Forests,
Khenchela,
Algeria.
E-mail: abdellah.menasri70@gmail.com

Abstract:

In this paper, we study the Lozi map by replacing the piecewise linear term in the first equation by the function max (f(x,y);g(x,y)) such that f and g are two arbitrary functions in R². This is a family model that allows us to study several new piecewise-smooth maps. We demonstrate that these models converge to a robust chaotic attractor and give some applications of these models in the real world.

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Paper's Title:

Higher Order Accurate Compact Schemes for Time Dependent Linear and Nonlinear Convection-Diffusion Equations

Author(s):

S. Thomas, Gopika P.B. and S. K. Nadupuri

Department of Mathematics
National Institute of Technology Calicut
Kerala
673601
India.
E-mail: sobinputhiyaveettil@gmail.com pbgopika@gmail.com nsk@nitc.ac.in
 

Abstract:

The primary objective of this work is to study higher order compact finite difference schemes for finding the numerical solution of convection-diffusion equations which are widely used in engineering applications. The first part of this work is concerned with a higher order exponential scheme for solving unsteady one dimensional linear convection-diffusion equation. The scheme is set up with a fourth order compact exponential discretization for space and cubic $C^1$-spline collocation method for time. The scheme achieves fourth order accuracy in both temporal and spatial variables and is proved to be unconditionally stable. The second part explores the utility of a sixth order compact finite difference scheme in space and Huta's improved sixth order Runge-Kutta scheme in time combined to find the numerical solution of one dimensional nonlinear convection-diffusion equations. Numerical experiments are carried out with Burgers' equation to demonstrate the accuracy of the new scheme which is sixth order in both space and time. Also a sixth order in space predictor-corrector method is proposed. A comparative study is performed of the proposed schemes with existing predictor-corrector method. The investigation of computational order of convergence is presented.

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Paper's Title:

Two Further Methods for Deriving Four Results Contiguous to Kummer's Second Theorem

Author(s):

I. Kim and J. Kim

Department of Mathematics Education,
Wonkwang University,
Iksan, 570-749,
Korea.
E-mail: iki@wku.ac.kr  

Department of Mathematics Education,
Wonkwang University,
Iksan, 570-749,
Korea.
E-mail: joohyung@wku.ac.kr
 

Abstract:

In the theory of generalized hypergeometric function, transformation and summation formulas play a key role. In particular, in one of the Kummer's transformation formulas, Kim, et al. in 2012, have obtained ten contiguous results in the form of a single result with the help of generalization of Gauss's second summation theorem obtained earlier by Lavoie, et al.. In this paper, we aim at presenting four of such results by the technique of contiguous function relations and integral method developed by MacRobert.

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Paper's Title:

A Note on Evaluation of a New Class of Integrals Involving Generalized Hypergeometric Function

Author(s):

Madhav Prasad Poudel, Dongkyu Lim^*, Narayan Prasad Pahari, Arjun K. Rathie

School of Engineering,
Pokhara University, Pokhara-30, Kaski,
Nepal.
E-mail: pdmadav@gmail.com

Department of Mathematics Education,
Andong National University, Andong 36729,
Republic of Korea.
E-mail: dklim@anu.ac.kr

Central Department of Mathematics,
Tribhuvan University, Kirtipur, Kathmandu,
Nepal.
E-mail: nppahari@gmail.com

Department of Mathematics,
Vedant College of Engineering & Technology (Rajasthan Technical University), Village: Tulsi,
Jakhamund, Dist. Bundi, Rajasthan State,
India.
E-mail: arjunkumarrathie@gmail.com

Abstract:

In the theory of hypergeometric and generalized hypergeometric series, classical summation theorems such as those of Gauss, Gauss second, Bailey and Kummer for the series ₂F₁; Watson, Dixon, Whipple and Saalshutz play a key role. Applications of the above mentioned summation theorems are well known for the series ₃F₂. In our present investigation, we aim to evaluate twenty five new class of integrals involving generalized hypergeometric function in the form of a single integral of the form:

The results are established with the help of the generalizations of the classical Watson's summation theorem obtained earlier by Lavoie et al.. Fifty interesting integrals in the form of two integrals (twenty five each) have also been given as special cases of our main findings.

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Paper's Title:

Positive Solutions of Evolution Operator Equations

Author(s):

Radu Precup

Department of Applied Mathematics,
Babes-Bolyai University,
Cluj, Romania

Abstract:

Existence and localization results are derived from Krasnoselskii’s compressionexpansion fixed point theorem in cones, for operator equations in spaces of continuous functions from a compact real interval to an abstract space. The main idea, first used in [12], is to handle two equivalent operator forms of the equation, one of fixed point type giving the operator to which Krasnoselskii’s theorem applies and an other one of coincidence type which is used to localize a positive solution in a shell. An application is presented for a boundary value problem associated to a fourth order partial differential equation on a rectangular domain.

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Paper's Title:

Orthogonality and ε-Orthogonality in Banach Spaces

Author(s):

H. Mazaheri and S. M. Vaezpour

Faculty of Mathematics, Yazd University, Yazd, Iran
vaezpour@yazduni.ac.ir 
hmazaheri@yazduni.ac.ir 

Abstract:

A concept of orthogonality on normed linear space was introduced by Brickhoff, also the concept of ε-orthogonality was introduced by Vaezpour. In this note, we will consider the relation between these concepts and the dual of X. Also some results on best coapproximation will be obtained.

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Paper's Title:

Positive Periodic Time-Scale Solutions for Functional Dynamic Equations

Author(s):

Douglas R. Anderson and Joan Hoffacker

Department of Mathematics and Computer Science
Concordia College
Moorhead, MN 56562 USA
andersod@cord.edu
URL: http://www.cord.edu/faculty/andersod/

Department of Mathematical Sciences
Clemson University
Clemson, SC 29634 USA
johoff@clemson.edu
URL: http://www.math.clemson.edu/facstaff/johoff.htm

Abstract:

Using Krasnoselskii's fixed point theorem, we establish the existence of positive periodic solutions to two pairs of related nonautonomous functional delta dynamic equations on periodic time scales, and then extend the discussion to higher-dimensional equations. Two pairs of corresponding nabla equations are also provided in an analogous manner.

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Paper's Title:

Normalized Truncated Levy models applied to the study of Financial Markets

Author(s):

M. C. Mariani, K. Martin, D. W. Dombrowski and D. Martinez

Department of Mathematical Sciences and Department of Finance,
New Mexico State University, P.O. Box 30001
Department 3MB Las Cruces, New Mexico 88003-8001
USA.
mmariani@nmsu.edu
kjmartin@nmsu.edu

Abstract:

This work is devoted to the study of the statistical properties of financial instruments from developed markets. We performed a new analysis of the behavior of companies corresponding to the DJIA index, and of the index itself, by using a normalized Truncated Levy walk model. We conclude that the Truncated Levy distribution describes perfectly the evolution of the companies and of the index near a crash.

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Paper's Title:

The Convergence of Modified Mann-Ishikawa Iterations when Applied to an Asymptotically Pseudocontractive Map

Author(s):

S. Soltuz

Departamento de Matematicas, Universidad de Los Andes, Carrera 1
No. 18A-10, Bogota,
Colombia
and
``T. Popoviciu" Institute of Numerical Analysis
Cluj-Napoca,
Romania
smsoltuz@gmail.com
URL:http://www.uniandes.edu.co/

Abstract:

We prove that under minimal conditions the modified Mann and Ishikawa iterations converge when dealing with an asymptotically pseudocontractive map. We give an affirmative answer to the open question from C.E. Chidume and H. Zegeye, Approximate fixed point sequences and convergence theorems for asymptotically pseudocontractive mappings, J. Math. Anal. Appl., 278 (2003), 354--366.

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Paper's Title:

Existence of Bounded Solutions for a Class of Strongly Nonlinear Elliptic Equations in Orlicz-Sobolev Spaces

Author(s):

Abdelmoujib Benkirane and Ahmed Youssfi

Department of Mathematics and Informatics, Faculty of Sciences Dhar El Mahraz
University Sidi Mohammed Ben Abdallah
PB 1796 Fez-Atlas, Fez
Morocco
a.benkirane@menara.ma
ahmed.youssfi@caramail.com

Abstract:

We prove, in the setting of Orlicz-Sobolev spaces, the existence of bounded solutions for some strongly nonlinear elliptic equations with operator of the principal part having degenerate coercivity and lower order terms not satisfying the sign condition. The data have a suitable summability and no Δ₂-condition is needed for the considered N-functions.

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Paper's Title:

Generalized Stieltjes Transform and its Fractional Integrals for Integrable Boehmian

Author(s):

Deshna Loonker and P. K. Banerji

Department Of Mathematics, Faculty Of Science,
J. N. V. University Jodhpur,
342 005,
India
deshnap@yahoo.com
banerjipk@yahoo.com

Abstract:

This paper investigates generalized Stieltjes transform for integrable Boehmian and further, generalized Stieltjes transform of fractional integrals are defined for integrable Boehmian.

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Paper's Title:

Certain Inequalities for P_Valent Meromorphic Functions with Alternating Coefficients Based on Integral Operator

Author(s):

A. Ebadian, S. Shams and Sh. Najafzadeh

Department of Mathematics, Faculty of Science
Urmia University, Urmia,
Iran
a.ebadian@mail.urmia.ac.ir
sa40shams@yahoo.com

Department of Mathematics, Faculty of Science
Maragheh University, Maragheh,
Iran
Shnajafzadeh@yahoo.com

Abstract:

In this paper we introduce the class of functions regular and  multivalent in the and satisfying

where is a linear operator.
Coefficient inequalities, distortion bounds, weighted mean and arithmetic mean of functions for this class have been obtained.

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Paper's Title:

Nontrivial Solutions of Singular Superlinear Three-point Boundary Value Problems at Resonance

Author(s):

Feng Wang, Fang Zhang

School of Mathematics and Physics,
Changzou University,
Changzhou, 213164,
China.
fengwang188@163.com

Abstract:

The singular superlinear second order three-point boundary value problems at resonance

are considered under some conditions concerning the first eigenvalues corresponding to the relevant linear operators, where n ∈ (0,1) is a constant, f is allowed to be singular at both t=0 and t=1. The existence results of nontrivial solutions are given by means of the topological degree theory.

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Paper's Title:

On Weighted Toeplitz Operators

Author(s):

S. C. Arora and Ritu Kathuria

Department of Mathematics,
University of Delhi,
Delhi 110007,
India.

Department of Mathematics,
Motilal Nehru College, University of Delhi,
Delhi 110021,
India.

ritu.kathuria@yahoo.co.in  

 

Abstract:

A weighted Toeplitz operator on H²(β) is defined as T_φf=P(φf) where P is the projection from L²(β) onto H²(β) and the symbol φ ∈ L²(β) for a given sequence β=‹β_n›_{n∈ Z} of positive numbers. In this paper, a matrix characterization of a weighted multiplication operator on L²β is given and it is used to deduce the same for a weighted Toeplitz operator. The eigenvalues of some weighted Toeplitz operators are also determined.

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Paper's Title:

On Generalized Triangle Inequality in p-Freéchet Spaces, 0<p<1

Author(s):

M. A. Latif

Department of Mathematics,
University of Hail, Hail,
Saudi Arabia
m_amer_latif@hotmail.com

Abstract:

In this paper generalized triangle inequality and its reverse in a p-Fréchet space where, 0<p<1 are obtained.

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Paper's Title:

On Reformations of 2--Hilbert Spaces

Author(s):

M. Eshaghi Gordji, A. Divandari, M. R. Safi and Y. J. Cho

Department of Mathematics, Semnan University,
P.O. Box 35195--363, Semnan,
Iran

meshaghi@semnan.ac.ir, madjid.eshaghi@gmail.com

Department of Mathematics, Semnan University,
Iran

Divandari@sun.Semnan.ac.ir

Department of Mathematics, Semnan University,
Iran

safi@semnan.ac.ir, SafiMohammadReza@yahoo.com

Department of Mathematics Education and the RINS,
Gyeongsang National University
Chinju 660-701,
Korea

yjcho@gnu.ac.kr

Abstract:

In this paper, first, we introduce the new concept of (complex) 2--Hilbert spaces, that is, we define the concept of 2--inner product spaces with a complex valued 2--inner product by using the 2--norm. Next, we prove some theorems on Schwartz's inequality, the polarization identity, the parallelogram laws and related important properties. Finally, we give some open problems related to 2--Hilbert spaces.

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Paper's Title:

On Some Estimates for the Logarithmic Mean

Author(s):

Shuhei Wada

Department of Information and Computer Engineering,
Kisarazu National College of Technology,
Kisarazu, Chiba 292-0041,
Japan.

E-mail: wada@j.kisarazu.ac.jp

Abstract:

We show some estimates for the logarithmic mean that are obtained from operator inequalities between the Barbour path and the Heinz means.

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Paper's Title:

Hermite-Hadamard-Fejer Type Inequalities for Harmonically s-convex Functions via Fractional Integrals

Author(s):

İmdat İşcan, Mehmet Kunt

Department of Mathematics,
Faculty of Sciences and Arts,
Giresun University, Giresun,
Turkey.
E-mail: imdat.iscan@giresun.edu.tr

Department of Mathematics,
Faculty of Sciences,
Karadeniz Technical University,
61080, Trabzon,
Turkey.
E-mail: mkunt@ktu.edu.tr

Abstract:

In this paper, some Hermite-Hadamard-Fejer type integral inequalities for harmonically s-convex functions in fractional integral forms have been obtained.

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Paper's Title:

Lower and Upper Bounds for the Point-Wise Directional Derivative of the Fenchel Duality Map

Author(s):

M. Raissouli^1,2, M. Ramezani³

¹Department of Mathematics,
Science Faculty, Taibah University,
P.O. Box 30097, Zip Code 41477, Al Madinah Al Munawwarah,
Saudi Arabia.

²Department of Mathematics,
Science Faculty, Moulay Ismail University, Meknes,
Morocco.
E-mail: raissouli.mustapha@gmail.com
 

³Department of Mathematics,
University of Bojnord, Bojnord,
Iran.
E-mail: m.ramezani@ub.ac.ir

Abstract:

In this paper, we introduce the point-wise directional derivative of the Fenchel duality map and we study its properties. The best lower and upper bounds of this point-wise directional derivative are also given. We explain how our functional results contain those related to the positive bounded linear operators.

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Paper's Title:

Birkhoff-James orthogonality and Best Approximant in L₁(X)

Author(s):

Mecheri Hacene and Rebiai Belgacem

Department of Mathematics and Informatics,
LAMIS laboratory, University of Tebessa,
Algeria.
E-mail: mecherih2000@yahoo.fr

Department of Mathematics and Informatics,
LAMIS laboratory, University of Tebessa,
Algeria.
E-mail: brebiai@gmail.com

Abstract:

Let X  be a complex Banach space and let (X,ρ) be a positive measure space. The Birkhoff-James orthogonality is a generalization of Hilbert space orthogonality to Banach spaces. We use this notion of orthogonality to establish a new characterization of Birkhoff-James orthogonality of bounded linear operators in L₁(X,ρ) also implies best approximation has been proved.

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Paper's Title:

New Exact Taylor's Expansions without the Remainder: Application to Finance

Author(s):

Moawia Alghalith

Economics Dept.,
University of the West Indies,
St Augustine,
Trinidad and Tobago.

E-mail: malghalith@gmail.com

Abstract:

We present new exact Taylor's expansions with fixed coefficients and without the remainder. We apply the method to the portfolio model.

Corrigendum.
A corrigendum for this article has been published. To view the corrigendum, please click here.

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Paper's Title:

Fractional class of analytic functions Defined Using q-Differential Operator

Author(s):

K . R. Karthikeyan, Musthafa Ibrahim and S. Srinivasan

Department of Mathematics and Statistics,
Caledonian College of Engineering, Muscat,
Sultanate of Oman.
E-mail: kr_karthikeyan1979@yahoo.com

College of Engineering,
University of Buraimi, Al Buraimi,
Sultanate of Oman.
E-mail: musthafa.ibrahim@gmail.com

Department of Mathematics, Presidency College (Autonomous),
Chennai-600005, Tamilnadu,
India.
 

Abstract:

We define a q-differential fractional operator, which generalizes Salagean and Ruscheweyh differential operators. We introduce and study a new class of analytic functions involving q-differential fractional operator. We also determine the necessary and sufficient conditions for functions to be in the class. Further, we obtain the coefficient estimates, extreme points, growth and distortion bounds.

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Paper's Title:

An Existence of the Solution to Neutral Stochastic Functional Differential Equations Under the Holder Condition

Author(s):

Young-Ho Kim

Department of Mathematics,
Changwon National University,
Changwon, Gyeongsangnam-do 51140,
Korea.

E-mail: iyhkim@changwon.ac.kr

Abstract:

In this paper, we show the existence and uniqueness of solution of the neutral stochastic functional differential equations under weakened H\"{o}lder condition, a weakened linear growth condition, and a contractive condition. Furthermore, in order to obtain the existence of a solution to the equation we used the Picard sequence.

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Paper's Title:

A New Adomian Approach to Solving Integral Equations of Fredholm and Volterra Second Kind

Author(s):

Ouedraogo Seny, Nebie Abdoul Wassiha, Youssouf Pare, Blaise Some

Departement de mathematiques,
Universite Joseph Ki-Zerbo,
Burkina Faso.
E-mail: oseny@yahoo.fr, nebwass@yahoo.fr
pareyoussouf@yahoo.fr, some@univ-ouaga.bf

Abstract:

In order to simplify the resolution of Fredholm and Volterra's second type integral equations, we propose a new approach based on the Adomian Decompositional Method (ADM). We test the new approach on several examples with success.

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Paper's Title:

Applications of Von Neumann Algebras to Rigidity Problems of (2-Step) Riemannian (Nil-)Manifolds

Author(s):

Atefeh Hasan-Zadeh and Hamid-Reza Fanai

DFouman Faculty of Engineering,
College of Engineering, University of Tehran,
Iran.
E-mail: hasanzadeh.a@ut.ac.ir

Department of Mathematical Sciences,
Sharif University of Technology,
Iran
E-mail: fanai@sharif.edu

Abstract:

In this paper, basic notions of von Neumann algebra and its direct analogues in the realm of groupoids and measure spaces have been considered. By recovering the action of a locally compact Lie group from a crossed product of a von Neumann algebra, other proof of one of a geometric propositions of O'Neil and an extension of it has been proposed. Also, using the advanced exploration of nilmanifolds in measure spaces and their corresponding automorphisms (Lie algebraic derivations) a different proof of an analytic theorem of Gordon and Mao has been attained. These two propositions are of the most important ones for rigidity problems of Riemannian manifolds especially 2-step nilmanifolds.

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Paper's Title:

An Efficient Modification of Differential Transform Method for Solving Integral and Integro-differential Equations

Author(s):

S. Al-Ahmad, Ibrahim Mohammed Sulaiman^*, and M. Mamat

Faculty of Informatics and Computing,
Universiti Sultan Zainal Abidin,
Terengganu, Besut Campus, 22200,
Malaysia.
E-mail: Alahmad.shadi@yahoo.com, ^*sulaimanib@unisza.edu.my, must@unisza.edu.my
 

Abstract:

In this paper, classes of integral and integro-differential equations are solved using a modified differential transform method. This proposed technique is based on differential transform method (DTM), Laplace transform (LT) procedure and Pad\'{e} approximants (PA). The proposed method which gives a good approximation for the true solution in a large region is referred to modified differential transform method (MDTM). An algorithm was developed to illustrate the flow of the proposed method. Some numerical problems are presented to check the applicability of the proposed scheme and the obtained results from the computations are compared with other existing methods to illustrates its efficiency. Numerical results have shown that the proposed MDTM method is promising compared to other existing methods for solving integral and integro-differential equations.

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Paper's Title:

Some Properties of (co)homology of Lie Algebra

Author(s):

Alaa Hassan Noreldeen Mohamed, Hegagi Mohamed Ali, Samar Aboquota

Department of Mathematics,
Faculty of Science,
Aswan University, Aswan,
Egypt.
E-mail: ala2222000@yahoo.com
hegagi_math@aswu.edu.eg
scientist_samar@yahoo.com

Abstract:

Lie algebra is one of the important types of algebras. Here, we studied lie algebra and discussed its properties. Moreover, we define the Dihedral homology of lie algebra and prove some relations among Hochschild, Cyclic and Dihedral homology of lie algebra. Finally, we prove the Mayer-vetories sequence on Dihedral homology of lie algebra and proved that .

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Paper's Title:

Hermite-Hadamard Type Inequalities for MN-Convex Functions

Author(s):

Sever S. Dragomir^1,2

¹Mathematics, College of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au

 
²DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL: https://rgmia.org/dragomir 

Abstract:

The present work endeavours to briefly present some of the fundamental results connected to the Hermite-Hadamard inequality for special classes of convex functions such as AG, AH, GA, GG, GH, HA, HG and HH -convex functions in which the author have been involved during the last five years. For simplicity, we call these classes of functions such as MN-convex functions, where M and N stand for any of the Arithmetic (A), Geometric (G) or Harmonic (H) weighted means of positive real numbers. The survey is intended for use by both researchers in various fields of Approximation Theory and Mathematical Inequalities, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.

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Paper's Title:

Existence and Approximation of Traveling Wavefronts for the Diffusive Mackey-Glass Equation

Author(s):

C. Ramirez-Carrasco and J. Molina-Garay

Facultad de Ciencias Basicas,
Universidad Catolica del Maule, Talca,
Chile
E-mail: carloshrc1989@gmail.com
 molina@imca.edu.pe

Abstract:

In this paper, we consider the diffusive Mackey-Glass model with discrete delay. This equation describes the dynamics of the blood cell production. We investigate the existence of traveling wavefronts solutions connecting the two steady states of the model. We develop an alternative proof of the existence of such solutions and we also demonstrate the existence of traveling wavefronts moving at minimum speed. The proposed approach is based on the use technique of upper-lower solutions. Finally, through an iterative procedure, we show numerical simulations that approximate the traveling wavefronts, thus confirming our theoretical results.

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Paper's Title:

A New Relaxed Complex-valued b-metric Type and Fixed Point Results

Author(s):

P. Singh, V. Singh and T. C. M. Jele

Department of Mathematics, University of KwaZulu-Natal,
Private Bag X54001, Durban,
South Africa.
E-mail: singhp@ukzn.ac.za
singhv@ukzn.ac.za
thokozani.jele@nwu.ac.za

Abstract:

In this paper, we study the existence and uniqueness of fixed point in complex valued b-metric spaces and introduce a new relaxed α, β Complex-valued b-metric type by relaxing the triangle inequality and determine whether the fixed point theorems are applicable in these spaces.

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Paper's Title:

A Generalization of a Partial b-metric and Fixed Point Theorems

Author(s):

Pravin Singh and Virath Singh

Department of Mathematics, University of KwaZulu-Natal,
Private Bag X54001, Durban,
South Africa.
E-mail: singhp@ukzn.ac.za
singhv@ukzn.ac.za

Abstract:

The purpose of this paper is to introduce the concept of a Partial α, β b-metric as a generalization of a partial b-metric and prove theorems for some contractive type mapping.

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Paper's Title:

The Boundedness of Gradient Solutions of P-Laplacian Type

Author(s):

Corina Karim, Khoirunisa, Ratno Bagus Edy Wibowo

Department of Mathematics,
Universitas Brawijaya,
Veteran Street, Malang,
Indonesia.
E-mail: co_mathub@ub.ac.id
khrnisa@student.ub.ac.id
rbagus@ub.ac.id

Abstract:

In this paper, we give the boundedness of gradient solutions result for p-Laplacian systems only in the singular case. The Lebesgue space for initial data belong to guarantee the local boundedness of gradient solutions.

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Paper's Title:

On the Oldest Problem in the Calculus of Variations: A New Message from Queen Dido

Author(s):

Olivier de La Grandville

Faculty of Economics,
Goethe University Frankfurt,
Theodore Adorno Platz 4, 60323 Frankfurt,
Germany.
E-mail: odelagrandville@gmail.com

Abstract:

We consider the problem of finding the optimal curve of given length linking two points in a plane such as it encloses a maximal area. We show that if the curve is not described by a single-valued function, its determination does not necessarily imply to work with a parametric representation of the curve. We show that a simpler approach is at hand -- and, who knows? -- this might well be the method Queen Dido used.

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Paper's Title:

A New Look at the Equations of the Calculus of Variations

Author(s):

Olivier de La Grandville

Faculty of Economics, Goethe University Frankfurt,
Theodore Adorno Platz 4, 60323 Frankfurt,
Germany.
E-mail: odelagrandville@gmail.com

Abstract:

We first offer an entirely new way to derive the celebrated Euler equation of the calculus of variations. The advantage of this approach is two-fold. On the one hand, it entirely eschews the two hurdles encountered by Lagrange, which become challenging in the case of elaborate functionals: getting rid of the arbitrary character of the perturbation given to the optimal function, and demonstrating the fundamental lemma of the calculus of variations. On the other hand, it leads in a direct way to the remarkable discovery made by Robert Dorfman ( 1969) when he introduced a modified Hamiltonian, which we called a Dorfmanian (2018) to honor his memory. In turn, extending the Dorfmanian enables to obtain readily the fundamental equations of the calculus of variations for the optimization of high-order functionals, or multiple integrals.

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Paper's Title:

Some Inequalities for the Generalized Riesz Potential on the Generalized Morrey Spaces over Hypergroups

Author(s):

I. Sihwaningrum, Renny, Y. Dasril

Jenderal Soedirman University,
Indonesia.
E-mail: idha.sihwaningrum@unsoed.ac.id renny@unsoed.ac.id
 

Universiti Tun Hussein Onn,
Malaysia.
E-mail: yosza@uthm.edu.my

Abstract:

We present in this paper some inequalities for the generalized Riesz potential on the generalized Morrey spaces over commutative hypergroups. The results can be found by employing the maximal operator.

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Paper's Title:

Asymptotic Behavior of Mixed Type Functional Equations

Author(s):

J. M. Rassias

Pedagogical Department, E.E., National and Capodistrian University of Athens, Section of Mathematics And Informatics, 4, Agamemnonos Str., Aghia Paraskevi, Athens 15342,Greece
jrassias@primedu.uoa.gr
URL: http://www.primedu.uoa.gr/~jrassias/

Abstract:

In 1983 Skof [24] was the first author to solve the Ulam problem for additive mappings on a restricted domain. In 1998 Jung [14] investigated the Hyers-Ulam stability of additive and quadratic mappings on restricted domains. In this paper we improve the bounds and thus the results obtained by Jung [14], in 1998 and by the author [21], in 2002. Besides we establish new theorems about the Ulam stability of mixed type functional equations on restricted domains. Finally, we apply our recent results to the asymptotic behavior of functional equations of different types.

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Paper's Title:

Reverses of the Triangle Inequality in Inner Product Spaces

Author(s):

Sever S. Dragomir

School of Computer Science and Mathematics,
Victoria University Of Technology,
PO Box 14428, Mcmc 8001,
Victoria, Australia.
sever@csm.vu.edu.au
Url: http://rgmia.vu.edu.au/SSDragomirWeb.html

Abstract:

Some new reverses for the generalised triangle inequality in inner product spaces are given. Applications in connection to the Schwarz inequality and for vector-valued integrals are provided as well.

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Paper's Title:

On the Ulam Stability for Euler-Lagrange Type Quadratic Functional Equations

Author(s):

Matina John Rassias and John Michael Rassias

Statistics and Modelling Science,
University of Strathclyde,
Livingstone Tower,
26 Richmond Str,
Glasgow, Uk, G1 1xh

Pedagogical Department, E. E., National and Capodistrian University of Athens,
Section of Mathematics and Informatics,
4, Agamemnonos Str, Aghia Paraskevi,
Athens 15342, Greece
 

Abstract:

In 1940 (and 1968) S. M. Ulam proposed the well-known Ulam stability problem. In 1941 D.H. Hyers solved the Hyers-Ulam problem for linear mappings. In 1951 D. G. Bourgin has been the second author treating the Ulam problem for additive mappings. In 1978 according to P.M. Gruber this kind of stability problems is of particular interest in probability theory and in the case of functional equations of different types. In 1982-2004 we established the Hyers-Ulam stability for the Ulam problem for different mappings. In 1992-2000 J.M. Rassias investigated the Ulam stability for Euler-Lagrange mappings. In this article we solve the Ulam problem for Euler-Lagrange type quadratic functional equations. These stability results can be applied in mathematical statistics, stochastic analysis, algebra, geometry, as well as in psychology and sociology.

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Paper's Title:

Solution of the Hyers-Ulam Stability Problem for Quadratic Type Functional Equations in Several Variables

Author(s):

John Michael Rassias

Pedagogical Department, E.E., National and Capodistrian University of Athens,
Section of Mathematics and Informatics,
4, Agamemnonos Str., Aghia Paraskevi,
Athens 15342,
Greece jrassias@primedu.uoa.gr
URL: http://www.primedu.uoa.gr/~jrassias/

Abstract:

In 1940 (and 1968) S. M. Ulam proposed the well-known Ulam stability problem. In 1941 D. H. Hyers solved the Hyers-Ulam problem for linear mappings. In 1951 D. G. Bourgin has been the second author treating the Ulam problem for additive mappings. In 1978 according to P. M. Gruber this kind of stability problems is of particular interest in probability theory and in the case of functional equations of different types. In 1982-2004 we established the Hyers-Ulam stability for the Ulam problem for different mappings. In this article we solve the Hyers-Ulam problem for quadratic type functional equations in several variables. These stability results can be applied in stochastic analysis, financial and actuarial mathematics, as well as in psychology and sociology.

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Paper's Title:

Merit Functions and Error Bounds for Mixed Quasivariational Inequalities

Author(s):

Muhammad Aslam Noor

Mathematics Department, COMSATS Institute of Information Technology,
Islamabad, Pakistan
noormaslam@hotmail.com

Abstract:

It is well known that the mixed quasivariational inequalities are equivalent to the fixed point problems. We use this equivalent alternative formulation to construct some merit functions for mixed quasivariational inequalities and obtain error bounds under some conditions. Since mixed quasivariational inequalities include the classical variational inequalities and the complementarity problems as special cases, our results continue to hold for these problems.

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Paper's Title:

Long Correlations Applied to the Study of Agricultural Indices in Comparison with the S&P500 index

Author(s):

M. C. Mariani, J. Libbin, M.P. Beccar Varela,
V. Kumar Mani, C. Erickson, D.J. Valles Rosales

Department of Mathematical Sciences,
Science Hall 236, New Mexico State University,
Las Cruces, NM 88003-8001,
USA.
mmariani@nmsu.edu 
 
 

Abstract:

Long-time correlations in agricultural indices are studied and their behavior is compared to the well-established S&P500 index. Hurst exponent and Detrended Fluctuation Analysis (DFA) techniques are used in this analysis. We detected long-correlations in the agricultural indices and briefly discussed some features specific in comparison to the S&P500 index.

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Paper's Title:

On ε-simultaneous Approximation in Quotient Spaces

Author(s):

H. Alizadeh, Sh. Rezapour, S. M. Vaezpour

Department of Mathematics, Aazad
Islamic University, Science and Research Branch, Tehran,
Iran

Department of Mathematics, Azarbaidjan
University of Tarbiat Moallem, Tabriz,
Iran

Department of Mathematics, Amirkabir
University of Technology, Tehran,
Iran

alizadehhossain@yahoo.com
sh.rezapour@azaruniv.edu
vaez@aut.ac.ir

URL:http://www.azaruniv.edu/~rezapour
URL:http://math-cs.aut.ac.ir/vaezpour

Abstract:

The purpose of this paper is to develop a theory of best simultaneous approximation to ε-simultaneous approximation. We shall introduce the concept of ε-simultaneous pseudo Chebyshev, ε-simultaneous quasi Chebyshev and ε-simultaneous weakly Chebyshev subspaces of a Banach space. Then, it will be determined under what conditions these subspaces are transmitted to and from quotient spaces.

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Paper's Title:

On Some Mapping Properties of Möbius Transformations

Author(s):

Nihal Yilmaz Özgür

Balkesir University, Faculty of Arts and Sciences, Department of Mathematics,
10145 Balkesir,
TURKEY
nihal@balikesir.edu.tr
URL: http://w3.balikesir.edu.tr/~nihal/

Abstract:

We consider spheres corresponding to any norm function on the complex plane and their images under the Möbius transformations. We see that the sphere preserving property is not an invariant characteristic property of Möbius transformations except in the Euclidean case.

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Paper's Title:

Some Open Problems in Analysis

Author(s):

A.G. Ramm

Mathematics Department, Kansas State University,
Manhattan, KS 66506-2602,
USA
ramm@math.ksu.edu
URL: http://www.math.ksu.edu/~ramm

Abstract:

In this paper some open problems in analysis are formulated. These problems were formulated and discussed by the author at ICMAA6.

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Paper's Title:

Asymptotic Distribution of Products of Weighted Sums of Dependent Random Variables

Author(s):

Y. Miao and J. F. Li

College of Mathematics and Information Science,
Henan Normal University
Henan, China
yumiao728@yahoo.com.cn

College of Mathematics and Information Science,
Henan Normal University, 453007
Henan, China.
junfen_li@yahoo.com.cn

Abstract:

In this paper we establish the asymptotic distribution of products of weighted sums of dependent positive random variable, which extends the results of Rempała and Wesołowski (2002).

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Paper's Title:

Fractional Integral Operators and Olsen Inequalities on Non-Homogeneous Spaces

Author(s):

Idha Sihwaningrum, Herry P. Suryawan, Hendra Gunawan

Analysis and Geometry Group,
Faculty of Mathematics and Natural Sciences,
Bandung Institute of Technology, Bandung 40132,
Indonesia
hgunawan@math.itb.ac.id
URL: http://personal.fmipa.itb.ac.id/hgunawan/

 

Abstract:

We prove the boundedness of the fractional integral operator I_α on generalized Morrey spaces of non-homogeneous type. In addition, we also present Olsen-type inequalities for a multiplication operator involving I_α. Our proof uses a result of García-Cuerva and Martell [3].

 

 

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Paper's Title:

Inclusion Properties of a Certain Subclass of Strongly Close-To-Convex Functions

Author(s):

S. M. Khairnar and M. More

Department of Mathematics,
Maharashtra Academy of Engineerring,
Alandi -412 105, Pune, Maharashtra,
INDIA.

smkhairnar2007@gmail.com, meenamores@gmail.com.
 

Abstract:

The purpose of this paper is to derive some inclusion and argument properties of a new subclass of strongly close-to-convex functions in the open unit disc. We have considered an integral operator defined by convolution involving hypergeometric function in the subclass definition. The subclass also extends to the class of α-spirallike functions of complex order.

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Paper's Title:

Trapping of Water Waves By Underwater Ridges

Author(s):

¹A. M. Marin, ¹R. D. Ortiz and ²J. A. Rodriguez-Ceballos.

¹Facultad de Ciencias Exactas y Naturales
Universidad de Cartagena
Sede Piedra de Bolivar, Avenida del Consulado
Cartagena de Indias, Bolivar,
Colombia.

²Instituto Tecnológico de Morelia Facultad de Ciencias Fisico Matematicas
Universidad Michoacana Tecnológico
1500, Col. Lomas de Santiaguito Edificio Be ,
Ciudad Universitaria, 58120 Morelia, Michoacan,
Mexico.

amarinr@unicartagena.edu.co, ortizo@unicartagena.edu.co.

URL: www.unicartagena.edu.co.

Abstract:

As is well-known, underwater ridges and submerged horizontal cylinders can serve as waveguides for surface water waves. For large values of the wavenumber in the direction of the ridge, there is only one trapped wave (this was proved in Bonnet & Joly (1993, SIAM J. Appl. Math. 53, pp 1507-1550)).
We construct the asymptotics of these trapped waves and their frequencies at high frequency by means of reducing the initial problem to a pair of boundary integral equations and then by applying the method of Zhevandrov & Merzon (2003, AMS Transl. (2) 208, pp 235-284), in order to solve them.

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Paper's Title:

Uniform Convergence of Schwarz Method for Noncoercive Variational Inequalities Simple Proof

Author(s):

M. Haiour and E. Hadidi.

Department of mathematics, LANOS Laboratory,
Faculty of the Sciences, University Badji Mokhtar,
P.O 23000 Annaba,
Algeria.

haiourm@yahoo.fr,
ehadidi71@yahoo.fr

Abstract:

In this paper we study noncoercive variational inequalities, using the Schwarz method. The main idea of this method consists in decomposing the domain in two subdomains. We give a simple proof for the main result concerning L^∞ error estimates, using the Zhou geometrical convergence and the L^∞ approximation given for finite element methods by Courty-Dumont.  

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Paper's Title:

A One-Line Derivation of the Euler and Ostrogradski Equations

Author(s):

Olivier de La Grandville

Stanford University,
Department of Management Science and Engineering,
Stanford, CA 94305,
U. S. A

ola@stanford.edu

Abstract:

At the very heart of major results of classical physics, the Euler and Ostrogradski equations have apparently no intuitive interpretation. In this paper we show that this is not so. Relying on Euler's initial geometric approach, we show that they can be obtained through a direct reasoning that does not imply any calculation. The intuitive approach we suggest offers two benefits: it gives immediate significance to these fundamental second-order non-linear differential equations; and second, it allows to obtain a property of the calculus of variations that does not seem to have been uncovered until now: the Euler and Ostrogradski equations can be derived not necessarily by giving a variation to the optimal function -- as is always done; one could equally well start by giving a variation to their derivative(s).

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Paper's Title:

C*-valued metric projection and Moore-Penrose inverse on Hilbert C*-modules

Author(s):

M. Eshaghi Gordji, H. Fathi and S.A.R. Hosseinioun

Department of Mathematics,
Semnan University, P.O. Box 35195-363, Semnan,
Iran.
Center of Excellence in Nonlinear Analysis and Applications (CENAA),
Semnan University,
Iran.
E-mail: Madjid.Eshaghi@gmail.com

Department of Mathematics,
Shahid Beheshti University, Tehran,
Iran.
E-mail: Hedayat.fathi@yahoo.com

Department of Mathematical Sciences,
University of Arkansas, Fayetteville, Arkansas 72701,
USA.
E-mail: shossein@uark.net

 

Abstract:

Let t be a regular operator between Hilbert C^*-modules and t^† be its Moore-Penrose inverse. We give some characterizations for t^† based on C^*-valued metric projection. Moore-Penrose inverse of bounded operators and elements of a C^*-algebra is studied as a special case.

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Paper's Title:

Weak Type Inequalities for Some Operators on Generalized Morrey Spaces Over Metric Measure Spaces

Author(s):

Idha Sihwaningrum, Ari Wardayani, Hendra Gunawan

Faculty of Mathematics and Natural Sciences,
Jenderal Soedirman University, Purwokerto 53122,
Indonesia.
E-mail: idha.sihwaningrum@unsoed.ac.id ariwardayani@yahoo.co.id

Faculty of Mathematics and Natural Sciences,
Bandung Institute of Technology, Bandung 40132,
Indonesia.
E-mail: hgunawan@math.itb.ac.id
URL: http://personal.fmipa.itb.ac.id/hgunawan/

 

Abstract:

We discuss weak type inequalities for maximal and fractional integral operators on generalized Morrey spaces over metric measure spaces. Here the measure satisfies the so called growth condition. By taking into account the maximal operator, we obtain a Hedberg type inequality, which leads us to the weak type inequality for the fractional integral operator on the same spaces.

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Paper's Title:

The boundedness of Bessel-Riesz operators on generalized Morrey spaces

Author(s):

Mochammad Idris, Hendra Gunawan and Eridani

Department of Mathematics,
Bandung Institute of Technology,
Bandung 40132,
Indonesia.
E-mail: mochidris@students.itb.ac.id

Department of Mathematics,
Bandung Institute of Technology,
Bandung 40132,
Indonesia.
E-mail: hgunawan@math.itb.ac.id
URL: http://personal.fmipa.itb.ac.id/hgunawan/

Department of Mathematics,
Airlangga University,
Surabaya 60115,
Indonesia.
E-mail: eridani.dinadewi@gmail.com

Abstract:

In this paper, we prove the boundedness of Bessel-Riesz operators on generalized Morrey spaces. The proof uses the usual dyadic decomposition, a Hedberg-type inequality for the operators, and the boundedness of Hardy-Littlewood maximal operator. Our results reveal that the norm of the operators is dominated by the norm of the kernels.

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Paper's Title:

Some interesting properties of finite continuous Cesàro operators

Author(s):

Abdelouahab Mansour and Abderrazak Hechifa

Operator theory laboratory (LABTHOP),
Eloued University,
Algeria.
E-mail: amansour@math.univ-lyon1.fr

Mathematics Department,
Faculty of Science,
Badji Mokhtar University, -Annaba,
Algeria.
E-mail: abderrazak02@gmail.com

Abstract:

A complex scalar λ is called an extended eigenvalue of a bounded linear operator T on a complex Banach space if there is a nonzero operator X such that TX = λ XT, the operator X is called extended eigenoperator of T corresponding to the extended eigenvalue λ.

In this paper we prove some properties of extended eigenvalue and extended eigenoperator for C₁ on L^p([0,1]), where C₁ is the Cesàro operator defined on the complex Banach spaces L^p([0 , 1])  for 1<p<∞ by the expression

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Paper's Title:

Partial Semigroup Algebras Associated to Partial Action

Author(s):

Bahman Tabatabaie Shourijeh and Sahar Moayeri Rahni

Department of Mathematics,
College of Sciences, Shiraz University,
Shiraz, 71454,
Iran.
E-mail: tabataba@math.susc.ac.ir

Department of Mathematics,
College of Sciences, Shiraz University,
Shiraz, 71454,
Iran.
E-mail: smoayeri@shirazu.ac.ir

Abstract:

For a given inverse semigroup S, we introduce the notion of algebraic crossed product by using a given partial action of S, and we will prove that under some condition it is associative. Also we will introduce the concept of partial semigroup algebra K_Par(S), and we show that the suitable quotient of K_Par(S) is a kind of crossed product.

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Paper's Title:

A Subordination Theorem for Analytic Functions

Author(s):

Marjono

Department of Mathematics, Faculty of Mathematics and Natural Sciences,
University of Brawijaya,
Jl. Veteran Malang 65145,
INDONESIA.
E-mail: marjono@ub.ac.id
URL: http://matematika.ub.ac.id

Abstract:

It is shown that if f is analytic in D={z:|z|<1}, with f(0)=f'(0)-1=0, then for implies where and that β(γ) is the largest number such that this implication holds.

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Paper's Title:

New Implicit Kirk-Type Schemes for General Class of Quasi-Contractive Operators in Generalized Convex Metric Spaces

Author(s):

K. Rauf, O. T. Wahab and A. Ali

Department of Mathematics,
University of Ilorin, Ilorin,
Nigeria.
E-mail: krauf@unilorin.edu.ng

Department of Statistics and Mathematical Sciences,
Kwara State University, Malete,
Nigeria.

Department of Mathematics,
Mirpur University of Science and Technology, Mirpur,
Pakistan.

Abstract:

In this paper, we introduce some new implicit Kirk-type iterative schemes in generalized convex metric spaces in order to approximate fixed points for general class of quasi-contractive type operators. The strong convergence, T-stability, equivalency, data dependence and convergence rate of these results were explored. The iterative schemes are faster and better, in term of speed of convergence, than their corresponding results in the literature. These results also improve and generalize several existing iterative schemes in the literature and they provide analogues of the corresponding results of other spaces, namely: normed spaces, CAT(0) spaces and so on.

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Paper's Title:

On Commutator of Aluthge Transforms and Fuglede-Putnam Property

Author(s):

(Manzar Maleki, Ali Reza Janfada and Seyed Mohammad Sadegh Nabavi Sales

International Campus, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad,
Iran.
E-mail: manzar.maleki@gmail.com
 

Faculty of Mathematics and Statistics, Department of Mathematics,
University of Birjand,
P. O. Box 414, Birjand 9717851367,
Iran.
E-mail: ajanfada@birjand.ac.ir

Department of Pure Mathematics, Hakim Sabzevari University,
P.O. Box 397, Sabzevar,
Iran.
E-mail: sadegh.nabavi@hsu.ac.ir

Abstract:

We deal with the well-known Fuglede-Putnam theorem and related FP-property. We show that if (A,B) has the FP-property, then so has where 0≤ t₁,t₂≤1 are arbitrary. We first prove that if and only if AX=XB for all X, whenever (A,B) has the FP-property. We prove some similar results for instead of $ as well. Also we introduce the sequence of generalized iterations of Aluthge transform of operators and express some results for this notion associated to the FP-property.

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Paper's Title:

Relations Between Differentiability And One-sided Differentiability

Author(s):

Q. D. Gjonbalaj, V. R. Hamiti and L. Gjoka

Department of Mathematics, Faculty of Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000, Kosova.
E-mail: qefsere.gjonbalaj@uni-pr.edu

{Department of Mathematics, Faculty of Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000, Kosova.
E-mail: valdete.rexhebeqaj@uni-pr.edu

Department of Mathematical Engineering,
Polytechnic University of Tirana, Tirana,
Albania
E-mail: luigjgjoka@ymail.com

Abstract:

In this paper, we attempt to approach to the problem of connection between differentiation and one-side differentiation in a more simple and explicit way than in existing math literature. By replacing the condition of differentiation with one-sided differentiation, more precisely with right-hand differentiation, we give the generalization of a theorem having to do with Lebesgue’s integration of derivative of a function. Next, based on this generalized result it is proven that if a continuous function has bounded right-hand derivative, then this function is almost everywhere differentiable, which implies that the set of points where the function is not differentiable has measure zero.

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Paper's Title:

A Low Order Least-Squares Nonconforming Finite Element Method for Steady Magnetohydrodynamic Equations

Author(s):

Z. Yu, D. Shi and H. Zhu

College of Science,
Zhongyuan University of Technology,
Zhengzhou 450007,
China.
E-mail: 5772@zut.edu.cn

School of Mathematics and Statistics,
Zhengzhou University,
Zhengzhou 450001,
China.
E-mail: shi_dy@126.com

Mathematics Department,
University of Southern Mississippi,
Hattiesburg MS, 39406,
U.S.A
E-mail: huiqing.zhu@usm.edu

Abstract:

A low order least-squares nonconforming finite element (NFE) method is proposed for magnetohydrodynamic equations with EQ₁^rot element and zero-order Raviart-Thomas element. Based on the above element's typical interpolations properties, the existence and uniqueness of the approximate solutions are proved and the optimal order error estimates for the corresponding variables are derived.

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Paper's Title:

Sweeping Surfaces with Darboux Frame in Euclidean 3-space E3

Author(s):

F. Mofarreh, R. Abdel-Baky and N. Alluhaibi

Mathematical Science Department, Faculty of Science,
Princess Nourah bint Abdulrahman University
Riyadh  11546,
Saudi Arabia.
E-mail: fyalmofarrah@pnu.edu.sa

 
Department of Mathematics, Faculty of Science,
University of Assiut,
Assiut 71516,
Egypt.
E-mail: rbaky@live.com

Department of Mathematics Science and Arts, College Rabigh Campus,
 King Abdulaziz University
Jeddah,
Saudi Arabia.
E-mail: nallehaibi@kau.edu.sa

Abstract:

The curve on a regular surface has a moving frame and it is called Darboux frame. We introduce sweeping surfaces along the curve relating to the this frame and investigate their geometrical properties. Moreover, we obtain the necessary and sufficient conditions for these surfaces to be developable ruled surfaces. Finally, an example to illustrate the application of the results is introduced.

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Paper's Title:

On General Class of Nonlinear Contractive Maps and their Performance Estimates

Author(s):

Olalekan Taofeek Wahab and Salaudeen Alaro Musa

Department of Mathematics and Statistics
Kwara State University, Malete
P. M. B. 1530 Ilorin,
Nigeria.
E-mail: taofeek.wahab@kwasu.edu.ng

Abstract:

This paper considers two independent general class of nonlinear contractive maps to study the existence properties of nonlinear operators with prior degenerate. The existence properties are proved in the framework of approximate fixed points with the imposition of the general class of contractive conditions in metrical convex spaces without emphasis on completeness or compactness. For computational purposes, the performance estimates and the sensitivity dependence of these conditions are obtained for the Picard operator. Practical examples are also considered to justify the validity of the conditions. The results ensure no term is lost in the operators with prior degenerate and the conditions are strictly larger class when compare with others in the literature.

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Paper's Title:

Additive Mappings on Semiprime Rings Functioning as Centralizers

Author(s):

Abu Zaid Ansari and Faiza Shujat

Department of Mathematics,
Faculty of Science,
Islamic University of Madinah, Madinah
K.S.A.
E-mail: ansari.abuzaid@gmail.com, ansari.abuzaid@iu.edu.sa

Department of Mathematics,
Faculty of Science,
Taibah University, Madinah,
K.S.A.
E-mail: faiza.shujat@gmail.com, fullahkhan@taibahu.edu.sa

Abstract:

The objective of this research is to prove that an additive mapping T:R → R is a centralizer on R if it satisfies any one of the following identities:

for all x ∈ R, where n ≥ 1 is a fixed integer and R is any suitably torsion free semiprime ring. Some results on involution "*" are also presented as consequences of the main theorems. In addition, we will take criticism in account with examples.

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Paper's Title:

Numerical Study of a Mathematical Model of a Free-Surface Potential Flow

Author(s):

H. Serguine, F. Guechi and A. Gasmi

Department Of Mathematics, Faculty of Science,
Ferhat Abbas Universty, 19000, Setif,
Algeria.
E-mail: houria.serguine@univ-msila.dz

 
Department Of Mathematics, Faculty of Science,
Ferhat Abbas Universty, 19000, Setif,
Algeria.
E-mail:  fairouz.chegaar@univ-setif.dz

Laboratory of Pure and Applied Mathematics, Faculty of Mathematics and Computer Science,
Mohamed Boudiaf Universty, 28000, M'sila,
Algeria.
E-mail: abdelkader.gasmi@univ-msila.dz

 

Abstract:

In this work, the problem of a potential and two-dimensional flow with a free surface of an incompressible, irrotational and inviscid fluid of a jet in front an inclined wall is considered, where γ is the inclination angle with the horizontal. The shape of the free surface is presented by curves which are found numerically by the series truncation method. This technique is based on the conformal transformations, resulting with the surface tension effect T with the boundary conditions on the free surfaces given by Bernoulli's equation. The found results are dependant on parameters which are: the Weber's number α and the angle γ. For each Weber's number value, only one solution is specified and some shapes of free surfaces of the jet are illustrated.

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Paper's Title:

On the Equiform Geometry of the Involute-evolute Curve Couple in Hyperbolic and de Sitter Spaces

Author(s):

M. Khalifa Saad, H. S. Abdel-Aziz and A. A. Abdel-Salam

Department of Mathematics,
Faculty of Science,
Islamic University of Madinah,
KSA.
E-mail: mohammed.khalifa@iu.edu.sa

Department of Mathematics,
Faculty of Science,
Sohag University, Sohag,
EGYPT.
E-mail: habdelaziz2005@yahoo.com

Department of Mathematics,
Faculty of Science,
Sohag University, Sohag,
EGYPT.
E-mail: asem2e@yahoo.com

Abstract:

In this paper, we aim to investigate the equiform differential geometric properties of the involute-evolute curve couple with constant equiform curvatures in three-dimensional hyperbolic and de Sitter spaces. Also, we obtain some relations between the curvature functions of these curves and investigate some special curves with respect to their equiform curvatures. Finally, we defray two computational examples to support our main findings.

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Paper's Title:

(p,q)-Lucas Polynomial and Their Applications to a Certain Family of Bi-univalent Functions Defined by Wanas Operator

Author(s):

M Musthafa Ibrahim, Saleem Ahmed

College of Engineering
University of Buraimi
Al Buraimi, P.O.Box 512,
Oman
E-mail: musthafa.i@uob.edu.om, saleem.a@uob.edu.om 

Abstract:

In this article, by making use of (p,q)-Lucas polynomials, we introduce and investigate a certain family of analytic and biunivalent functions associated with Wanas operator which defined in the open unit disk U. Also, the upper bounds for the initial Taylor-Maclaurin coefficients and the Fekete-Szegö inequality of functions belonging to this family are obtained.

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Paper's Title:

Lebesgue Absolutely Continuous Functions Taking Values on C[a,b]

Author(s):

Andrew Felix IV Suarez Cunanan

North Eastern Mindanao State University
E-mail: afccunanan@nemsu.edu.ph

Abstract:

In this paper a version of absolutely continuous function using Lebesgue partition instead of Riemann partition over the field of C[a,b] will be introduced and we call this function as Lebesgue absolutely continuous function on [f,g]. Moreover, some properties of Lebesgue absolutely continuous function on [f,g] will be presented together with its relationship with the other continuous functions.

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Paper's Title:

Fekete-Szegö Inequality for Certain Class of Analytic Functions

Author(s):

V. Ravichandran, Maslina Darus, M. Hussain Khan, and  K. G. Subramanian

School of Mathematical Sciences, Universiti Sains Malaysia,
11800 Usm, Penang, Malaysia
vravi@cs.usm.my

School of Mathematical Sciences, Faculty of Sciences and Technology,
Ukm, Banki 43600, Malaysia
maslina@pkrisc.cc.ukm.my

Department of Mathematics, Islamiah College,
Vaniambadi 635 751, India

Department of Mathematics, Madras Christian College, Tambaram,
Chennai- 600 059, India
kgsmani@vsnl.net

Abstract:

In this present investigation, the authors obtain Fekete-Szegö inequality for a certain class of analytic functions f(z) for which lies in a region starlike with respect to 1 and symmetric with respect to the real axis. Also certain application of our main result for a class of functions defined by Hadamard product (convolution) is given. As a special case of our result we obtain Fekete-Szegö inequality for a class of functions defined through fractional derivatives. Also we obtain Fekete-Szegö inequality for the inverse functions.

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Paper's Title:

On a Criteria for Strong Starlikeness

Author(s):

V. Ravichandran, M. Darus, and N. Seenivasagan

School Of Mathematical Sciences, Universiti Sains Malaysia,
11800 Usm Penang, Malaysia
vravi@cs.usm.my
URL: http://cs.usm.my/~vravi

School of Mathematical Sciences, Faculty of Sciences and Technology,
Ukm, Bangi 43600, Malaysia
maslina@pkrisc.cc.ukm.my

Sindhi College, 123, P. H. Road, Numbal,
Chennai 600 077 India
vasagan2000@yahoo.co.in
 

Abstract:

In this paper, we are concerned with finding sufficient condition for certain normalized analytic function f(z) defined on the open unit disk in the complex plane to be strongly starlike of order  α. Also we have obtained similar results for certain functions defined by Ruscheweyh derivatives and Sălăgean derivatives. Further extension of these results are given for certain p-valent analytic functions defined through a linear operator.

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Paper's Title:

Multivalued Hemiequilibrium Problems

Author(s):

Muhammad Aslam Noor

Mathematics Department,
COMSATS Institute of Information Technology,
Sector H-8/1, Islamabad,
Pakistan.
noormaslam@hotmail.com

 

Abstract:

In this paper, we introduce and study a new class of equilibrium problems, known as multivalued hemiequilibrium problems. The auxiliary principle technique is used to suggest and analyze some new classes of iterative algorithms for solving multivalued hemiequilibrium problems. The convergence of the proposed methods either requires partially relaxed strongly monotonicity or pseudomonotonicity. As special cases, we obtain a number of known and new results for solving various classes of equilibrium and variational inequality problems. Since multivalued hemiequilibrium problems include hemiequilibrium, hemivariational inequalities, variational inequalities and complementarity problems as specials cases, our results still hold for these problems.

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Paper's Title:

Some Approximation for the linear combinations of modified Beta operators

Author(s):

Naokant Deo

Department of Applied Mathematics
Delhi College of Engineering
Bawana Road, Delhi - 110042,
India.
dr_naokant_deo@yahoo.com

Abstract:

In this paper, we propose a sequence of new positive linear operators β_n to study the ordinary approximation of unbounded functions by using some properties of the Steklov means.

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Paper's Title:

Logarithmically complete monotonicity properties for the gamma functions

Author(s):

Chao-Ping Chen and Feng Qi

Department of Applied Mathematics and Informatics,
Research Institute of Applied Mathematics,
Henan Polytechnic University,
Jiaozuo City, Henan 454010,
China.
chenchaoping@hpu.edu.cn

Department of Applied Mathematics and Informatics,
Research Institute of Applied Mathematics,
Henan Polytechnic University,
Jiaozuo City, Henan 454010,
China.
qifeng@hpu.edu.cn
fengqi618@member.ams.org

Abstract:

Some logarithmically completely monotonic functions involving the gamma functions are presented. As a consequence, some known results are proved and refined.

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Paper's Title:

q-Norms are Really Norms

Author(s):

H. Belbachir, M. Mirzavaziri and M. S. Moslehian

USTHB, Faculté de Mathématiques,
B.P. 32, El Alia, 16111,
Bab Ezzouar, Alger,
Algérie.
hbelbachir@usthb.dz

Department of Mathematics,
Ferdowsi University, P. O. Box 1159,
Mashhad 91775, Iran.
mirzavaziri@math.um.ac.ir
URL: http://www.mirzavaziri.com

Department of Mathematics,
Ferdowsi University,
P. O. Box 1159,
Mashhad 91775, Iran.
moslehian@ferdowsi.um.ac.ir
URL: http://www.um.ac.ir/~moslehian/

Abstract:

Replacing the triangle inequality, in the definition of a norm, by , we introduce the notion of a q-norm. We establish that every q-norm is a norm in the usual sense, and that the converse is true as well.

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Paper's Title:

Komatu Integral Transforms of Analytic Functions Subordinate to Convex Functions

Author(s):

T. N. Shanmugam and C. Ramachandran

Department of Mathematics, College of Engineering,
Anna University, Chennai-600 025, Tamilnadu,
India
shan@annauniv.edu

Department of Mathematics, College of Engineering,
Anna University, Chennai-600 025, Tamilnadu,
India
crjsp2004@yahoo.com

Abstract:

In this paper, we consider the class A of the functions f(z) of the form

which are analytic in an open disk and study certain subclass of the class A, for which

has some property. Certain inclusion and the closure properties like convolution with convex univalent function etc. are studied.

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Paper's Title:

Weighted Generalization of the Trapezoidal Rule via Fink Identity

Author(s):

S. Kovač, J. Pečarić and A. Vukelić

Faculty of Geotechnical Engineering, University of Zagreb,
Hallerova aleja 7, 42000 Varaždin,
Croatia.
sanja.kovac@gtfvz.hr

Faculty of Textile Technology, University of Zagreb,
Pierottijeva 6, 10000 Zagreb,
Croatia.
pecaric@hazu.hr

Faculty of Food Technology and Biotechnology, Mathematics department, University of Zagreb,
Pierottijeva 6, 10000 Zagreb,
Croatia.
avukelic@pbf.hr

Abstract:

The weighted Fink identity is given and used to obtain generalized weighted trapezoidal formula for n-time differentiable functions. Also, an error estimate is obtained for this formula.

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Paper's Title:

A Sum Form Functional Equation and Its Relevance in Information Theory

Author(s):

Prem Nath and Dhiraj Kumar Singh

Department of Mathematics
University of Delhi
Delhi - 110007
India
pnathmaths@gmail.com
dksingh@maths.du.ac.in

Abstract:

The general solutions of a sum form functional equation containing four unknown mappings have been investigated. The importance of these solutions in relation to various entropies in information theory has been emphasised.

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Paper's Title:

Positive Solutions for Systems of Three-point Nonlinear Boundary Value Problems

Author(s):

J. Henderson and S. K. Ntouyas

Department of Mathematics, Baylor University
Waco, Texas
76798-7328 USA.
Johnny_Henderson@baylor.edu
URL: http://www3.baylor.edu/~Johnny_Henderson

Department of Mathematics, University of Ioannina
451 10 Ioannina,
Greece.
sntouyas@cc.uoi.gr
URL: http://www.math.uoi.gr/~sntouyas

Abstract:

Values of λ are determined for which there exist positive solutions of the system of three-point boundary value problems, u''(t)+ λa(t)f(v(t))=0, v''(t)+λb(t)g(u(t))=0, for 0 < t <1, and satisfying, u(0) = 0, u(1)=α u(η), v(0) = 0, v(1)=α v(η). A Guo-Krasnosel'skii fixed point theorem is applied.

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Paper's Title:

On Some Remarkable Product of Theta-function

Author(s):

M. S. Mahadeva Naika, M. C. Maheshkumar and K. Sushan Bairy

Department of Mathematics,
Bangalore University, Central College Campus,
Bangalore-560 001,
INDIA
msmnaika@rediffmail.com
softmahe@rediffmail.com
ksbairy@gmail.com

Abstract:

On pages 338 and 339 in his first notebook, Ramanujan records eighteen values for a certain product of theta-function. All these have been proved by B. C. Berndt, H. H. Chan and L-C. Zhang [4]. Recently M. S. Mahadeva Naika and B. N. Dharmendra [7, 8] and Mahadeva Naika and M. C. Maheshkumar [9] have obtained general theorems to establish explicit evaluations of Ramanujan's remarkable product of theta-function. Following Ramanujan we define a new function b_M,N as defined in (1.5). The main purpose of this paper is to establish some new general theorems for explicit evaluations of product of theta-function.

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Paper's Title:

Some Generalized Difference Sequence Spaces Defined by Orlicz Functions

Author(s):

Ramzi S. N. Alsaedi and Ahmad H. A. Bataineh

Department of Mathematics, King Abdul Aziz University,
Jeddah P.O.Box 80203,
Saudia Arabia
ramzialsaedi@yahoo.co.uk

Department of Mathematics, Al al-Bayt University,
Mafraq 25113,
Jordan
ahabf2003@yahoo.ca

Abstract:

In this paper, we define the sequence spaces: [V,M,p,u,Δ ],[V,M,p,u,Δ]₀ and [V,M,p,u,Δ]_∞, where for any sequence x=(x_n), the difference sequence Δx is given by Δx=(Δx_n) = (x_n-x_n-1) . We also study some properties and theorems of these spaces. These are generalizations of those defined and studied by Savas and Savas and some others before.

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Paper's Title:

Integer Sums of Powers of Trigonometric Functions (MOD p), for prime p

Author(s):

G. J. Tee

Department of Mathematics, University of Auckland, Auckland,
New Zealand
tee@math.auckland.ac.nz

Abstract:

Many multi--parameter families of congruences (mod p) are found for integer sums of  q^th powers of the trigonometric functions over various sets of equidistant arguments, where p is any prime factor of q. Those congruences provide sensitive tests for the accuracy of software for evaluating trigonometric functions to high precision.

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Paper's Title:

A Double Inequality for Divided Differences and Some Identities of the Psi and Polygamma Functions

Author(s):

B. N. Guo and F. Qi

School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province, 454010, China
bai.ni.guo@gmail.com, bai.ni.guo@hotmail.com

School of Research Institute of Mathematical Inequality Theory, Henan Polytechnic University, Jiaozuo City, Henan Province, 454010, China
qifeng618@gmail.com, qifeng618@hotmail.com, qifeng618@qq.com
URL:http://qifeng618.spaces.live.com

Abstract:

In this short note, from the logarithmically completely monotonic property of the function , a double inequality for the divided differences and some identities of the psi and polygamma functions are presented.

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Paper's Title:

On a Method of Proving the Hyers-Ulam Stability of Functional Equations on Restricted Domains

Author(s):

Janusz Brzdęk

Department of Mathematics
 Pedagogical University Podchorąźych 2,
30-084 Kraków,
Poland
jbrzdek@ap.krakow.pl

Abstract:

We show that generalizations of some (classical) results on the Hyers-Ulam stability of functional equations, in several variables, can be very easily derived from a simple result on stability of a functional equation in single variable

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Paper's Title:

A Coincidence Theorem for Two Kakutani Maps

Author(s):

Mircea Balaj

Department of Mathematics,
University of Oradea,
410087, Oradea,
Romania.
 mbalaj@uoradea.ro

Abstract:

In this paper we prove the following theorem: Let X be a nonempty compact convex set in a locally convex Hausdorff topological vector space, D be the set of its extremal points and F,T: X―◦X two Kakutani maps; if for each nonempty finite subset A of D and for any x ∈ coA, F (x) ∩ coA ≠ Ø, then F and T have a coincidence point. The proof of this theorem is given first in the case when X is a simplex, then when X is a polytope and finally in the general case. Several reformulations of this result are given in the last part of the paper.

 

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Paper's Title:

Improvement of Jensen's Inequality for Superquadratic Functions

Author(s):

S. Abramovich, B. Ivanković, and J. Pečarić

Department of Mathematics,
University of Haifa,
Haifa 31905,
Israel.
abramos@math.haifa.ac.il

Faculty of Transport and Trafic Engineering,
University of Zagreb,
Vukelićeva 4, 10000,
Croatia
bozidar.ivankovic@zg.t-com.hr

Faculty of Textile,
University of Zagreb,
Prilaz Baruna Filipovića 30, 10000 Zagreb,
Croatia
pecaric@element.hr

 

Abstract:

Since 1907, the famous Jensen's inequality has been refined in different manners. In our paper, we refine it applying superquadratic functions and separations of domains for convex functions. There are convex functions which are not superquadratic and superquadratic functions which are not convex. For superquadratic functions which are not convex we get inequalities analogue to inequalities satisfied by convex functions. For superquadratic functions which are convex (including many useful functions) we get refinements of Jensen's inequality and its extensions.

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Paper's Title:

Some Inequalities for Gramian Normal Operators and for Gramian Self-Adjoint Operators in Pseudo-Hilbert Spaces

Author(s):

Loredana Ciurdariu

Department of Mathematics,"Politehnica" University of Timisoara,
P-ta. Victoriei, No.2, 300006-Timisoara,
ROMANIA
cloredana43@yahoo.com.

Abstract:

Several inequalities for gramian normal operators and for gramian self-adjoint operators in pseudo-Hilbert spaces are presented.

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Paper's Title:

Hardy Type Inequalities via Convexity - The Journey so Far

Author(s):

 James A. Oguntuase and Lars-Erik Persson

 Department of Mathematics, University of Agriculture,
 P. M. B. 2240, Abeokuta, Nigeria.

Department of Mathematics, Luleå University of Technology,
SE-971 87, Luleå , Sweden.

oguntuase@yahoo.com, larserik@sm.luth.se .
 

Abstract:

It is nowadays well-known that Hardy's inequality (like many other inequalities) follows directly from Jensen's inequality. Most of the development of Hardy type inequalities has not used this simple fact, which obviously was unknown by Hardy himself and many others. Here we report on some results obtained in this way mostly after 2002 by mainly using this fundamental idea.  

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Paper's Title:

Sharp L^p Improving Results for Singular Measures on Cⁿ⁺¹

Author(s):

E. Ferreyra, M. Urciuolo

FaMAF-CIEM,
Universidad Nacional de Córdoba-Conicet,
Ciudad Universitaria, 5000 Córdoba,
Argentina

eferrey@famaf.unc.edu.ar
urciuolo@famaf.unc.edu.ar

Abstract:

For j=1,...,n, let Ω_j be open sets of the complex plane and let φ_j be holomorphic functions on Ω_j such that φ_j^'' does not vanish identically on Ω_j. We consider φ(z₁,...,z_n) =φ₁(z₁) +...+φ_n(z_n). We characterize the pairs (p,q) such that the convolution operator with the surface measure supported on a compact subset of the graph of φ is p-q bounded.

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Paper's Title:

On the Inequality

Author(s):

A. Coronel and F. Huancas

Departamento de Ciencias Básicas,
Facultad de Ciencias, Universidad del Bío-Bío, Casilla 447,
Campus Fernando May, Chillán, Chile.

acoronel@roble.fdo-may.ubiobio.cl

Departamento Académico de Matemática,
Facultad de Ciencias Físicas y Matemáticas,
Universidad Nacional Pedro Ruiz Gallo, Juan XIII s/n,
Lambayeque, Perú

fihuanca@gmail.com
 

Abstract:

In this paper we give a complete proof of for all positive real numbers a, b and c. Furthermore, we present another way to prove the statement for

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Paper's Title:

L∞- Error Estimate of Schwarz Algorithm for Elliptic Quasi-Variational Inequalities Related to Impulse Control Problem

Author(s):

Saadi Samira and Mehri Allaoua

Lab. LANOS, Department of Mathematics,
University Badji Mokhtar Annaba,
P.O.Box 12, Annaba 23000,
Algeria.

Lab. LAIG, Department of Mathematics,
University May 8th 1945,
P.O.Box 401, Guelma 24000,
Algeria.

E-mail: saadisamira69@yahoo.fr
allmehri@yahoo.fr

Abstract:

In this work, we study Schwarz method for a class of elliptic quasi-variational inequalities. The principal result of this investigation is to prove the error estimate in ∞-norm for two domains with overlapping nonmatching grids, using the geometrical convergence, and the uniform convergence of Cortey Dumont.

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Paper's Title:

Hyponormal and K-Quasi-Hyponormal Operators On Semi-Hilbertian Spaces

Author(s):

Ould Ahmed Mahmoud Sid Ahmed and Abdelkader Benali

Mathematics Department,
College of Science,
Aljouf University,
Aljouf 2014,
Saudi Arabia.
E-mail: sididahmed@ju.edu.sa

Mathematics Department, Faculty of Science,
Hassiba Benbouali, University of Chlef,
B.P. 151 Hay Essalem, Chlef 02000,
Algeria.
E-mail: benali4848@gmail.com

Abstract:

Let H be a Hilbert space and let A be a positive bounded operator on H. The semi-inner product < u|v>_A:=<Au|v>, u,v ∈ H induces a semi-norm || .||_A on H. This makes H into a semi-Hilbertian space. In this paper we introduce the notions of hyponormalities and k-quasi-hyponormalities for operators on semi Hilbertian space (H,||.||_A), based on the works that studied normal, isometry, unitary and partial isometries operators in these spaces. Also, we generalize some results which are already known for hyponormal and quasi-hyponormal operators. An operator T ∈ B_A (H) is said to be (A, k)-quasi-hyponormal if

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Paper's Title:

Mapped Chebyshev Spectral Methods for Solving Second Kind Integral Equations on the Real Line

Author(s):

Ahmed Guechi and Azedine Rahmoune

Department of Mathematics, University of Bordj Bou Arréridj,
El Anasser, 34030, BBA,
Algeria.
E-mail: a.guechi2017@gmail.com
E-mail: a.rahmoune@univ-bba.dz

Abstract:

In this paper we investigate the utility of mappings to solve numerically an important class of integral equations on the real line. The main idea is to map the infinite interval to a finite one and use Chebyshev spectral-collocation method to solve the mapped integral equation in the finite interval. Numerical examples are presented to illustrate the accuracy of the method.

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Paper's Title:

On an extension of Edwards's double integral with applications

Author(s):

I. Kim, S. Jun, Y. Vyas and A. K. Rathie

Department of Mathematics Education,
Wonkwang University,
Iksan, 570-749,
Republic of Korea.

General Education Institute,
Konkuk University,
Chungju 380-701,
Republic of Korea.

Department of Mathematics, School of Engineering,
Sir Padampat Singhania University,
Bhatewar, Udaipur, 313601, Rajasthan State,
India.

Department of Mathematics,
Vedant College of Engineering and Technology,
(Rajasthan Technical University),
Bundi-323021, Rajasthan,
India.

E-mail: iki@wku.ac.kr sjun@kku.ac.kr
yashoverdhan.vyas@spsu.ac.in arjunkumarrathie@gmail.com

Abstract:

The aim of this note is to provide an extension of the well known and useful Edwards's double integral. As an application, new class of twelve double integrals involving hypergeometric function have been evaluated in terms of gamma function. The results are established with the help of classical summation theorems for the series ₃F₂ due to Watson, Dixon and Whipple. Several new and interesting integrals have also been obtained from our main findings.

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Paper's Title:

A new approach to the study of fixed point for simulation functions with application in G-metric spaces

Author(s):

Komi Afassinou and Ojen Kumar Narain

Department of Mathematical Sciences, University of Zululand,
KwaDlangezwa,
South Africa.
E-mail: komia@aims.ac.za

School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: naraino@ukzn.ac.za

Abstract:

The purpose of this work is to generalize the fixed point results of Kumar et al. [11] by introducing the concept of (α,β)-Z-contraction mapping, Suzuki generalized (α,β)-Z-contraction mapping, (α,β)-admissible mapping and triangular (α,β)-admissible mapping in the frame work of G-metric spaces. Fixed point theorems for these class of mappings are established in the frame work of a complete G-metric spaces and we establish a generalization of the fixed point result of Kumar et al. [11] and a host of others in the literature. Finally, we apply our fixed point result to solve an integral equation.

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Paper's Title:

Oblique Projectors from the Simpson Discrete Fourier Transformation Matrix

Author(s):

P. Singh and V. Singh

School of Mathematics, Computer Science and Statistics,
University of Kwazulu-Natal,
Private Bag X54001, Durban 4001,
South Africa.
E-mail: singhp@ukzn.ac.za, singhv@ukzn.ac.za

Abstract:

In this paper we examine the projectors of the Simpson Discrete Fourier Transform matrix of dimension two modulus four and show how they decompose the complex vector space into a direct sum of oblique eigenspaces. These projection operators are used to define a Simpson Discrete Fractional Fourier Transform (SDFRFT).

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Paper's Title:

Estimates of Norms on Krein Spaces

Author(s):

Satheesh K. Athira, P. Sam Johnson and K. Kamaraj

Department of Mathematical and Computational Sciences,
National Institute of Technology Karnataka,
Surathkal, Mangaluru 575 025,
India.
E-mail: athirachandri@gmail.com

Department of Mathematical and Computational Sciences,
National Institute of Technology Karnataka,
Surathkal, Mangaluru 575 025,
India.
E-mail:sam@nitk.edu.in

Department of Mathematics,
University College of Engineering Arni,
Anna University, Arni 632 326,
India.
E-mail: krajkj@yahoo.com

Abstract:

Various norms can be defined on a Krein space by choosing different underlying fundamental decompositions. Some estimates of norms on Krein spaces are discussed and a few results in Bognar's paper are generalized.

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Paper's Title:

Hankel Functional Connected to Lemniscate of Bernoulli

Author(s):

K. Ramanuja Rao, Rajnesh Lal and Kaushal Singh

Fiji National University,
Department of Mathematics & Statistics,
P.O. Box 5529, Lautoka,
Fiji.
E-mail: ramanuja.kotti@fnu.ac.fj
 rajnesh.lal@fnu.ac.fj
kaushal.singh@fnu.ac.fj

Abstract:

The aim of present paper is to derive a higher bound (HB) of 3^rd order Hankel determinant for a collection of holomorphic mappings connected with exactly to the right side of the lemniscate of Bernoulli, whose polar coordinates form is r² = 2cos²(2θ). The method carried in this paper is more refined than the method adopted by the authors (see [1]), who worked on this problem earlier.

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Paper's Title:

Multistage Analytical Approximate Solution of Quasi-Linear Differential- Algebraic System of Index Two

Author(s):

Ibrahim M. Albak, F. A. Abdullah^* and Zarita Zainuddin

School of Mathematical Sciences,
 Universiti Sains Malaysia,
 11800 USM, Penang,
Malaysia.
E-mail:  ibra13975@gmail.com,
farahaini@usm.my,
zarita@usm.my

Abstract:

In this paper, a new Multistage Transform Method (MSDTM) has been proposed by utilizing a well-known transformation technique, the Differential Transform Method (DTM), to solve Differential Algebraic Equations (DAEs) with index 2. The advantage of the proposed scheme is that it does not require an index reduction and extends the convergence domain of the solution. Some examples for various types of problems are carried out to show the ability of MSDTM in solving DAEs. The results obtained are in good agreement with the existing literature which demonstrates the effectiveness and efficiency of the proposed method.

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Paper's Title:

Bounds for the Extremal Eigenvalues of Positive Definite Matrices

Author(s):

Shivani Singh and Pravin Singh

Unisa, Department of Decision Sciences,
PO Box 392,
Pretoria,
0003,
South Africa.
E-mail: singhs2@unisa.ac.za

University of KwaZulu-Natal,
School of Mathematics Statistics and Computer Sciences
Private Bag X54001,
Durban,
4000,
South Africa.
E-mail: singhprook@gmail.com

Abstract:

We use a projection to achieve bounds for a vector function of the eigenvalues of a positive definite matrix. For various choices of the monotonic function we are able to obtain bounds for the extremal eigenvalues in terms of the traces of the matrix and its powers. These bounds are relatively simple to compute.

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Paper's Title:

Results on Bounds of the Spectrum of Positive Definite Matrices by Projections

Author(s):

P. Singh, S. Singh, V. Singh

University of KwaZulu-Natal,
Private Bag X54001,
Durban, 4001,
South Africa.
E-mail: singhp@ukzn.ac.za

University of South Africa, Department of Decision Sciences,
PO Box 392, Pretoria, 0003,
South Africa.
E-mail: singhs2@unisa.ac.za

University of KwaZulu-Natal,
Private Bag X54001,
Durban, 4001,
South Africa.
E-mail: singhv@ukzn.ac.za

Abstract:

In this paper, we develop further the theory of trace bounds and show that in some sense that the earlier bounds obtained by various authors on the spectrum of symmetric positive definite matrices are optimal. Our approach is by considering projection operators, from which several mathematical relationships may be derived. Also criteria for positive lower bounds are derived.

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Paper's Title:

Recursive Bounds for the Eigenvalues of Symmetric Positive Definite Matrices

Author(s):

Pravin Singh, Shivani Singh, Virath Singh

University of KwaZulu-Natal,
Private Bag X54001,
Durban, 4001,
South Africa.

University of South Africa,
Department of Decision Sciences, PO Box 392,
 Pretoria,0003,
South Africa.

University of KwaZulu-Natal,
Private Bag X54001,
Durban, 4001,
South Africa.

E-mail: singhp@ukzn.ac.za, singhs2@unisa.ac.za, singhv@ukzn.ac.za
 

Abstract:

In this paper, we bound the extremal eigenvalues of a positive definite real symmetric matrix by considering a part of the characteristic equation in the region of the smallest and largest eigenvalues. An expansion around these values leads to a sequence of monotonic functions, whose zeros coincide with the extremal zeros of associated polynomials. The latter is shown to yield bounds that are fairly accurate.

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Paper's Title:

Semicommutative and Semiprime Properties in Bi-amalgamated Rings

Author(s):

¹A. Aruldoss, ²C. Selvaraj, ³G. E. Chatzarakis, ⁴S. L. Panetsos, ⁵U. Leerawat

¹ Department of Mathematics,
Mepco Schlenk Engineering College,
Sivakasi-626 005, Tamilnadu,
India.
aruldossa529@gmail.com

² Department of Mathematics,
Periyar University,
Salem - 636 011, Tamilnadu,
India.
selvavlr@yahoo.com

 ^3,4 Department of Electrical and Electronic Engineering Educators,
School of Pedagogical and Technological Education (ASPETE),
Marousi 15122, Athens,
Greece.
geaxatz@otenet.gr spanetsos@aspete.gr

⁵ Department of Mathematics,
Faculty of Science, Kasetsart University,
Bangkok 10900,
Thailand.
fsciutl@ku.ac.th

Abstract:

Let α: A→ B and β: A→ C be two ring homomorphisms and I and I' be two ideals of B and C, respectively, such that α^{-1}(I)=β^{-1}(I'). In this paper, we give a characterization for the bi-amalgamation of A with (B, C) along (I, I') with respect to (α, β) (denoted by A⋈^{(α, β)}(I, I')) to be a SIT, semiprime, semicommutative and semiregular. We also give some characterization for these rings.

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Paper's Title:

Pseudomonotonicity and Quasimonotonicity by Translations versus Monotonicity in Hilbert Spaces

Author(s):

George Isac and Dumitru Motreanu

Department of Mathematics, Royal Military College of Canada, P.O. Box 17000 Stn Forces
Kingston, Ontario, Canada, K7k 7b4.
gisac@juno.com

Département de Mathématiques, Université de Perpignan, 66860 Perpignan, France.
motreanu@univ-perp.fr

Abstract:

Let  be a Gâteaux differentiable mapping on an open convex subset  of a Hilbert space. If there exists a straight line  such that  is pseudomonotone for any  then  is monotone. Related results using a regularity condition are given.

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Paper's Title:

Positive Solution For Discrete Three-Point Boundary Value Problems

Author(s):

Wing-Sum Cheung And Jingli Ren

Department of Mathematics,
The University of Hong Kong,
Pokfulam, Hong Kong
wscheung@hku.hk

Institute of Systems Science,
Chinese Academy of Sciences,
Beijing 100080, P.R. China
renjl@mx.amss.ac.cn

Abstract:

This paper is concerned with the existence of positive solution to the discrete three-point boundary value problem

,

where , and f is allowed to change sign. By constructing available operators, we shall apply the method of lower solution and the method of topology degree to obtain positive solution of the above problem for on a suitable interval. The associated Green’s function is first given.

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Paper's Title:

Generalizations of two theorems on absolute summability methods

Author(s):

H.S. Özarslan and H.N. Öğdük

Department of Mathematics,
Erciyes University, 38039 Kayseri,
Turkey
seyhan@erciyes.edu.tr
nogduk@erciyes.edu.tr
URL: http://fef.erciyes.edu.tr/math/hikmet.htm
 

 

Abstract:

In this paper two theorems on summability methods, which generalize two theorems of Bor on summability methods, have been proved.

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Paper's Title:

Essential Random Fixed Point Set of Random Operators

Author(s):

Ismat Beg

Centre for Advanced Studies in Mathematics,
Lahore University of Management Sciences (LUMS),
54792-Lahore, PAKISTAN. ibeg@lums.edu.pk
URL: http://web.lums.edu.pk/~ibeg

Abstract:

We obtain necessary and sufficient conditions for the existence of essential random fixed point of a random operator defined on a compact metric space. The structure of the set of essential random fixed points is also studied.

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Paper's Title:

Inverse problems for parabolic equations

Author(s):

A. G. Ramm

Mathematics Department,
Kansas State University,
Manhattan, KS 66506-2602,
USA
ramm@math.ksu.edu
URL: http://www.math.ksu.edu/~ramm

Abstract:

Let  in , where  is a bounded domain with a smooth connected boundary , ,  is the delta-function. Assume that ,  on . Given the extra data , , can one find ,  and  Here  is some number. An answer to this question and a method for finding ,  and  are given.

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Paper's Title:

Parameter dependence of the solution of second order nonlinear ODE's via Perov's fixed point theorem

Author(s):

A. M. Bica, S. Muresan and G. Grebenisan

University of Oradea,
Str. Armatei Romane no.5, 410087,
Oradea, Romania.
smbica@yahoo.com
smuresan@uoradea.ro
grebe@uoradea.ro

Abstract:

Using the Perov's fixed point theorem, the smooth dependence by parameter of the solution of a two point boundary value problem corresponding to nonlinear second order ODE's is obtained.

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Paper's Title:

Uniqueness of Meromorphic Functions that Share Three Values

Author(s):

Abhijit Banerjee

Department of Mathematics
Kalyani Government Engineering College
West Bengal 741235
India.
abanerjee_kal@yahoo.co.in
abanerjee@mail15.com
abanerjee_kal@rediffmail.com

Abstract:

In the paper dealing with the uniqueness problem of meromorphic functions we prove five theorems one of which will improve a result given by Lahiri \cite{5} and the remaining will supplement some previous results.

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Paper's Title:

The Voronovskaja Type Theorem for the Stancu Bivariate Operators

Author(s):

Ovidiu T. Pop

National College "Mihai Eminescu",
5 Mihai Eminescu Street,
Satu Mare 440014, Romania

Vest University "Vasile Goldis" of Arad, Branch of Satu Mare,
26 Mihai Viteazul Street
Satu Mare 440030, Romania
ovidiutiberiu@yahoo.com

Abstract:

In this paper, the Voronovskaja type theorem for the Stancu bivariate operators is established. As particular cases, we shall obtain the Voronovskaja type theorem for the Bernstein and Schurer operators.

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Paper's Title:

On Some Ramanujan's Schläfli Type Modular Equations

Author(s):

K. R. Vasuki

Department of Mathematics, Acharya Institute of Technology, Soldevanahalli,
Chikkabanavara (Post), Hesaragatta Main Road, Bangalore-560 090,
INDIA.
vasuki_kr@hotmail.com

Abstract:

In this paper, we give new proof of certain Ramanujan-Schläfli modular equations. We also obtain a new modular equation of degree 23.

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Paper's Title:

On Segal's Quantum Option Pricing

Author(s):

Andreas Boukas

Department of Mathematics and Natural Sciences,
American College of Greece
Aghia Paraskevi 15342, Athens,
Greece.
andreasboukas@acgmail.gr

Abstract:

We apply the non-commutative extension of classical Itô stochastic calculus, known as quantum stochastic calculus, to the quantum Black-Scholes model in the sense of Segal and Segal [4]. Explicit expressions for the best quantum option price and the associated optimal quantum portfolio are derived.

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Paper's Title:

On a Subclass of Uniformly Convex Functions Defined by the Dziok-Srivastava Operator

Author(s):

M. K. Aouf and G. Murugusundaramoorthy

Mathematics Department, Faculty of Science,
Mansoura University 35516,
Egypt.
mkaouf127@yahoo.com

School of Science and Humanities, VIT University
Vellore - 632014,
India.
gmsmoorthy@yahoo.com

Abstract:

Making use of the Dziok-Srivastava operator, we define a new subclass T^l_m([α₁];α,β) of uniformly convex function with negative coefficients. In this paper, we obtain coefficient estimates, distortion theorems, locate extreme points and obtain radii of close-to-convexity, starlikeness and convexity for functions belonging to the class T^l_m([α₁];α,β) . We consider integral operators associated with functions belonging to the class H^l_m([α₁];α,β) defined via the Dziok-Srivastava operator. We also obtain several results for the modified Hadamard products of functions belonging to the class T^l_m([α₁];α,β) and we obtain properties associated with generalized fractional calculus operators.

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Paper's Title:

Maximal Inequalities for Multidimensionally Indexed Demimartingales and the Hájek-Rényi Inequality for Associated Random Variables

Author(s):

Tasos C. Christofides and Milto Hadjikyriakou

Department of Mathematics and Statistics
University of Cyprus
P.O.Box 20537, Nicosia 1678, Cyprus

tasos@ucy.ac.cy
miltwh@gmail.com

Abstract:

Demimartingales and demisubmartingales introduced by Newman and
Wright (1982) generalize the notion of martingales and
submartingales respectively. In this paper we define
multidimensionally indexed demimartingales and demisubmartingales
and prove a maximal inequality for this general class of random
variables. As a corollary we obtain a Hájek-Rényi inequality
for multidimensionally indexed associated random variables, the bound of which, when reduced to the case of single index, is sharper than the bounds already known in the literature.

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Paper's Title:

The Best Upper Bound for Jensen's Inequality

Author(s):

Vasile Cirtoaje

Department of Automatic Control and Computers
University of Ploiesti
Romania.

vcirtoaje@upg-ploiesti.ro.

Abstract:

In this paper we give the best upper bound for the weighted Jensen's discrete inequality applied to a convex function f defined on a closed interval I in the case when the bound depends on f, I and weights. In addition, we give a simpler expression of the upper bound, which is better than existing similar one.

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Paper's Title:

Refinements of the Trace Inequality of Belmega, Lasaulce and Debbah

Author(s):

Shigeru Furuichi and Minghua Lin

Department of Computer Science and System Analysis,
College of Humanities and Sciences, Nihon University,
3-25-40, Sakurajyousui, Setagaya-ku, Tokyo, 156-8550, Japan.
 

Department of Mathematics and Statistics,
 University of Regina, Regina, Saskatchewan, Canada S4S 0A2.

furuichi@chs.nihon-u.ac.jp, lin243@uregina.ca.

Abstract:

 In this short paper, we show a certain matrix trace inequality and then give a refinement of the trace inequality proven by Belmega, Lasaulce and Debbah. In addition, we give an another improvement of their trace inequality.

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Paper's Title:

A Generalization of a Trace Inequality for Positive Definite Matrices

Author(s):

E. V. Belmega, M. Jungers, and S. Lasaulce

Université Paris-Sud Xi, SUPELEC,
Laboratoire Des Signaux Et Systèmes,
Gif-Sur-Yvette,
France.

belmega@lss.supelec.fr
http://veronica.belmega.lss.supelec.fr

CNRS, ENSEM, CRAN, Vandoeuvre,
France.

marc.jungers@cran.uhp-nancy.fr
http://perso.ensem.inpl-nancy.fr/Marc.Jungers/

CNRS, SUPELEC, Laboratoire des Signaux et Systèmes,
Gif-Sur-Yvette,
France.

lasaulce@lss.supelec.fr
http://samson.lasaulce.lss.supelec.fr

Abstract:

In this note, we provide a generalization of the trace inequality derived in [Belmega].

More precisely, we prove that for arbitrary K ≥ 1 where Tr(∙) denotes the matrix trace operator, A₁, B₁ are any positive definite matrices and A_k, B_k for all k∈{2,...,k}, are any positive semidefinite matrices.

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Paper's Title:

Bounds for Two Mappings Associated to the Hermite-Hadamard Inequality

Author(s):

S. S. Dragomir^1,2 and I. Gomm¹

¹Mathematics, School of Engineering & Science,
Victoria University,
PO Box 14428, Melbourne City, MC 8001,
Australia.

²School of Computational & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa.

sever.dragomir@vu.edu.au
ian.gomm@vu.edu.au
URL: http://rgmia.org/dragomir  
 

Abstract:

Some inequalities concerning two mappings associated to the celebrated Hermite-Hadamard integral inequality for convex function with applications for special means are given.

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Paper's Title:

Some Inequalities Concerning Derivative and Maximum Modulus of Polynomials

Author(s):

N. K. Govil, A. Liman and W. M. Shah

Department of Mathematics & Statistics, 
Auburn University, Auburn,
Alabama 36849-5310,
U.S.A

Department of Mathematics,
National Institute of Technology,
Srinagar, Kashmir,
India - 190006

Department of Mathematics,
Kashmir University,
Srinagar, Kashmir,
India - 190006

govilnk@auburn.edu
abliman22@yahoo.com
wmshah@rediffmail.com

 
 

Abstract:

In this paper, we prove some compact generalizations of some well-known Bernstein type inequalities concerning the maximum modulus of a polynomial and its derivative in terms of maximum modulus of a polynomial on the unit circle. Besides, an inequality for self-inversive polynomials has also been obtained, which in particular gives some known inequalities for this class of polynomials. All the inequalities obtained are sharp.

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Paper's Title:

On the Three Variable Reciprocity Theorem and Its Applications

Author(s):

D. D. Somashekara and D. Mamta

Department of Studies in Mathematics,
University of Mysore,
Manasagangotri, Mysore-570 006
India
dsomashekara@yahoo.com 

Department of Mathematics,
The National Institute of Engineering,
Mysore-570 008,
India
mathsmamta@yahoo.com  
 

Abstract:

In this paper we show how the three variable reciprocity theorem can be easily derived from the well known two variable reciprocity theorem of Ramanujan by parameter augmentation. Further we derive some q-gamma, q-beta and eta-function identities from the three variable reciprocity theorem.

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Paper's Title:

On Generalization of Hardy-type Inequalities

Author(s):

K. Rauf, S. Ponnusamy and J. O. Omolehin  

Department of Mathematics,
University of Ilorin, Ilorin,
Nigeria
krauf@unilorin.edu.ng

Department of Mathematics,
Indian Institute of Technology Madras,
Chennai- 600 036,
India
samy@iitm.ac.in

Department of Mathematics,
University of Ilorin, Ilorin,
Nigeria
omolehin_joseph@yahoo.com

Abstract:

This paper is devoted to some new generalization of Hardy-type integral inequalities and the reversed forms. The study is to determine conditions on which the generalized inequalities hold using some known hypothesis. Improvement of some inequalities are also presented.

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Paper's Title:

Some Identities for Ramanujan - Göllnitz - Gordon Continued fraction

Author(s):

M. S. Mahadeva Naika, B. N. Dharmendra and S. Chandan Kumar

Department of Mathematics,
Bangalore University,
Central College Campus,
Bangalore-560 001,
INDIA

msmnaika@rediffmail.com

chandan.s17@gmail.com 

Department of Mathematics,
Maharani's Science College for Women,
J. L. B. Road, Mysore-570 001,
INDIA

dharmamath@rediffmail.com 

Abstract:

In this paper, we obtain certain P--Q eta--function identities, using which we establish identities providing modular relations between Ramanujan-Göllnitz-Gordon continued fraction H(q) and H(q^n) for n= 2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 17, 19, 23, 25, 29 and 55.

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Paper's Title:

Multilinear Fractional Integral Operators on Herz Spaces

Author(s):

Yasuo Komori-Furuya

School of High Technology and Human Welfare,
Tokai University, 317 Nishino Numazu Shizuoka, 410-0395
Japan

komori@wing.ncc.u-tokai.ac.jp

Abstract:

We prove the boundedness of the multilinear fractional integral operators of Kenig and Stein type on Herz spaces. We also show that our results are optimal.

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Paper's Title:

On the Biharmonic Equation with Nonlinear Boundary Integral Conditions

Author(s):

R. Hamdouche and H. Saker

L.M.A. Department of Mathematics, Faculty of Sciences,
University of Badji Mokhtar,
P.O.Box 12. Annaba 23000,
Algeria.
E-mail: h_saker@yahoo.fr, hmdch.rahma16@gmail.com

 

Abstract:

In the present work, we deal with the biharmonic problems in a bounded domain in the plane with the nonlinear boundary integral conditions. After applying the Boundary integral method, a system of nonlinear boundary integral equations is obtained. The result show that when the nonlinearity satisfies some conditions lead the existence and uniqueness of the solution.

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Paper's Title:

Some New Inequalities of Hermite-Hadamard and Fejér Type for Certain Functions with Higher Convexity

Author(s):

Steven G. From

Department of Mathematics,
University of Nebraska at Omaha,
Omaha, Nebraska 68182-0243,
U.S.A.
E-mail: sfrom@unomaha.edu

Abstract:

In this paper, we present some new inequalities of Hermite-Hadamard or Fejér type for certain functions satisfying some higher convexity conditions on one or more derivatives.
An open problem is given also.
Some applications to the logarithmic mean are given.

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Paper's Title:

Applications of the Structure Theorem of (w₁,w₂)-Tempered Ultradistributions

Author(s):

Hamed M. Obiedat and Lloyd E. Moyo

Department of Mathematics,
Hashemite University,
P.O.Box 150459, Zarqa13115,
Jordan.
E-mail: hobiedat@hu.edu.j

Department of Mathematics, Computer Science & Statistics,
Henderson State University,
1100 Henderson Street, Arkadelphia, AR 71999,
USA.
E-mail: moyol@hsu.edu

Abstract:

Using a previously obtained structure theorem for (w₁, w₂)-tempered ultradistributions, we prove that these ultradistributions can be represented as initial values of solutions of the heat equation.

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Paper's Title:

Existence of Positive Solutions for Nonlinear Fractional Differential Equations with Multi-point Boundary Conditions

Author(s):

N. Adjeroud

Khenchela University, Department of Mathematics,
Khenchela, 40000,
Algeria.
E-mail: adjnac@gmail.com

Abstract:

This paper is devoted to the existence results of positive solutions for a nonlinear fractional differential equations with multi-point boundary conditions. By means of the Schauder fixed point theorem, some results on the existence are obtained.

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Paper's Title:

Euler Series Solutions for Linear Integral Equations

Author(s):

Mostefa Nadir and Mustapha Dilmi

Department of Mathematics,
University of Msila 28000,
ALGERIA.
E-mail: mostefanadir@yahoo.fr
E-mail: dilmiistapha@yahoo.fr

Abstract:

In this work, we seek the approximate solution of linear integral equations by truncation Euler series approximation. After substituting the Euler expansions for the given functions of the equation and the unknown one, the equation reduces to a linear system, the solution of this latter gives the Euler coefficients and thereafter the solution of the equation. The convergence and the error analysis of this method are discussed. Finally, we compare our numerical results by others.

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Paper's Title:

Introducing the Dorfmanian: A Powerful Tool for the Calculus Of Variations

Author(s):

Olivier de La Grandville

Department of Management Science and Engineering,
Stanford University,
475 Via Ortega, Stanford, CA 94305,
U. S. A.

E-mail: odelagrandville@gmail.com

Abstract:

We show how a modified Hamiltonian proposed by Robert Dorfman [1] to give intuitive sense to the Pontryagin maximum principle can be extended to easily obtain all high-order equations of the calculus of variations. This new concept is particularly efficient to determine the differential equations leading to the extremals of functionals defined by n-uple integrals, while a traditional approach would require -- in some cases repeatedly -- an extension of Green's theorem to n-space.
Our paper is dedicated to the memory of Robert Dorfman (1916 - 2002).

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Paper's Title:

Invariant Subspaces Close to Almost Invariant Subspaces for Bounded Linear Operators

Author(s):

M. A. Farzaneh, A. Assadi and H. M. Mohammadinejad

Department of Mathematical and Statistical Sciences,
University of Birjand,
PO Box 97175/615, Birjand,
Iran.
E-mail: farzaneh@birjand.ac.ir

Department of Mathematical and Statistical Sciences,
University of Birjand,
PO Box 97175/615, Birjand,
Iran.
E-mail: assadi-aman@birjand.ac.ir

Department of Mathematical and Statistical Sciences,
University of Birjand,
PO Box 97175/615, Birjand,
Iran.
E-mail: hmohammadin@birjand.ac.ir

Abstract:

In this paper, we consider some features of almost invariant subspace notion. At first, we restate the notion of almost invariant subspace and obtain some results. Then we try to achieve an invariant subspace completely close to an almost invariant subspace. Also, we introduce the notion of  "almost equivalent subspaces"  to simply the subject related to almost invariant subspaces and apply it.

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Paper's Title:

Local Boundedness of Weak Solutions for Singular Parabolic Systems of p-Laplacian Type

Author(s):

Corina Karim, Marjono

Department of Mathematics,
Universitas Brawijaya,
Indonesia.
E-mail:  co_mathub@ub.ac.id, marjono@ub.ac.id

Abstract:

We study the local boundedness of weak solutions for evolutional p-Laplacian systems in the singular case. The initial data is belonging to Lebesgue space L^∞ (0,T;W^(1,p) (Ω,Rⁿ )). We use intrinsic scaling method to treat the boundedness of weak solutions. The main result is to make the local boundedness of weak solution for the systems well-worked in the intrinsic scaling.

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Paper's Title:

A Generalization of Ostrowski's Inequality for Functions of Bounded Variation via a Parameter

Author(s):

Seth Kermausuor

Department of Mathematics and Computer Science,
Alabama State University,
Montgomery, AL 36101,
USA.
E-mail: skermausour@alasu.edu

Abstract:

In this paper, we provide a generalization of the Ostrowski's inequality for functions of bounded variation for k points via a parameter λ∈[0,1]. As a by product, we consider some particular cases to obtained some interesting inequalities in these directions. Our results generalizes some of the results by Dragomir in [S. S. DRAGOMIR, The Ostrowski inequality for mappings of bounded variation, Bull. Austral. Math. Soc., 60 (1999), pp. 495--508.]

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Paper's Title:

Riemann-Stieltjes Integrals and Some Ostrowski Type Inequalities

Author(s):

W. G. Alshanti

Department of General Studies,
Jubail University College,
KSA.
E-mail: shantiw@ucj.edu.sa

Abstract:

In this article, we investigate new integral inequalities of Ostrowski's type of various functional aspects. For mapping's second derivative, we assume two cases, namely, L₁ and L_∞ spaces. Moreover, for first derivative, we investigate two different characteristics, namely, bounded variation and locally Lipchitz continuity. Applications to special means and composite quadrature rules are also carried out.

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Paper's Title:

Coefficient Estimates Of Sakaguchi Kind Functions Using Lucas Polynomials

Author(s):

H. Priya and B. Srutha Keerthi

Department of Mathematics,
School of Advanced Sciences,
VIT Chennai Campus,
Chennai - 600 048,
India.
E-mail: priyaharikrishnan18@gmail.com

Department of Mathematics,
School of Advanced Sciences,
VIT Chennai Campus,
Chennai - 600 048,
India.
E-mail: isruthilaya06@yahoo.co.in

Abstract:

By means of (p,q) Lucas polynomials, we estimate coefficient bounds and Fekete-Szego inequalities for functions belonging to this class. Several corollaries and consequences of the main results are also obtained.

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Paper's Title:

Existence of Compositional Square Roots of Circle Maps

Author(s):

K. Ali Akbar and T. Mubeena

Department of Mathematics,
School of Physical Sciences,
Central University of Kerala,
Periya - 671320,
Kasaragod,
Kerala,
India.
E-mail:  aliakbar.pkd@gmail.com, aliakbar@cukerala.ac.in

Department of Mathematics,
School of Mathematics and Computational Sciences,
University of Calicut,
Thenhipalam-673635,
Malappuram,
Kerala,
India.
E-mail: mubeenatc@gmail.com, mubeenatc@uoc.ac.in

Abstract:

In this paper, we discuss the existence of compositional square roots of circle maps. If f and g are two maps such that g ○ g = f, we say that g is a compositional square root of f.

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Paper's Title:

Simple Integral Representations for the Fibonacci and Lucas Numbers

Author(s):

Seán M. Stewart

Physical Science and Engineering Division,
King Abdullah University of Science and Technology,
Thuwal 23955-6900,
Saudi Arabia.
E-mail: sean.stewart@kaust.edu.sa

Abstract:

Integral representations of the Fibonacci numbers F_{kn + r} and the Lucas numbers L_{kn + r} are presented. Each is established using methods that rely on nothing beyond elementary integral calculus.

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Paper's Title:

Preserver of Local Spectrum of Skew-product Operators

Author(s):

Rohollah Parvinianzadeh^1,*, Meysam Asadipour² and Jumakhan Pazhman³

¹Department of Mathematics,
College of Sciences,
University of Yasouj,
Yasouj, 75918-74934,
Iran.
E-mail: r.parvinian@yu.ac.ir

²Department of Mathematics,
College of Sciences,
University of Yasouj,
Yasouj, 75918-74934,
Iran.
E-mail: Asadipour@yu.ac.ir

³Department of Mathematics,
Ghor Institute of higher education,
Afghanistan.
E-mail: jumapazhman@gmail.com

Abstract:

Let H and K be infinite-dimensional complex Hilbert spaces, and B(H) (resp. B(K)) be the algebra of all bounded linear operators on H (resp. on K). For an operator T∈ B(H) and a vector h∈ H, let σ_T(h) denote the local spectrum of T at h. For two nonzero vectors h₀∈ H and k₀∈ K, we show that if two maps φ₁ and φ₂ from B(H) into B(K) satisfy

σ_{φ1(T)φ2(S)*}(k₀)= σ_TS*(h₀})

for all T, S ∈ B(H), and their range containing all operators of rank at most two, then there exist bijective linear maps P : H→ K and Q : K→ H such that φ₁(T) = PTQ and φ₂(T)^* =Q^-1T^*P^-1 for all T ∈ B(H). Also, we obtain some interesting results in this direction.

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Paper's Title:

New Refinements for Integral and Sum Forms of Generalized Hölder Inequality For N Term

Author(s):

M. Jakfar, Manuharawati, D. Savitri

Mathematics Department,
Universitas Negeri Surabaya
Jalan Ketintang Gedung C8, Surabaya, 60321
Indonesia.
E-mail: muhammadjakfar@unesa.ac.id
manuharawati@unesa.ac.id
diansavitri@unesa.ac.id

Abstract:

We know that in the field of functional analysis, Hölder inequality is very well known, important, and very applicable. So many researchers are interested in discussing these inequalities. Many world mathematicians try to improve these inequalities. In general, the Hölder inequality has two forms, namely the integral form and the sum form. In this paper, we will introduce a new refinement of the generalization of Hölder inequalities in both integral and addition forms. Especially in the sum form, improvements will be introduced that are better than the previous improvements that have been published by Jing-feng Tian, Ming-hu Ha, and Chao Wang.

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Paper's Title:

Differential Equations for Indicatrices, Spacelike and Timelike Curves

Author(s):

Sameer, Pradeep Kumar Pandey

Department of Mathematics,
Jaypee University of Information Technology,
Solan, Himachal Pradesh,
India.
E-mail: sksameer08@gmail.com, pandeypkdelhi@gmail.com 

Abstract:

Motivated by the recent work of Deshmukh et al. [20], in this paper we show that Tangent, Binormal, and Principal Normal indicatrices do not form non-trivial differential equations. Finally, we obtain the 4th-order differential equations for spacelike and timelike curves.

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Paper's Title:

Corrigendum for Differential Equations for Indicatrices, Spacelike and Timelike Curves

Author(s):

Sameer, Pradeep Kumar Pandey

Department of Mathematics,
Jaypee University of Information Technology,
Solan, Himachal Pradesh,
India.
E-mail: sksameer08@gmail.com, pandeypkdelhi@gmail.com 

ABSTRACT NOT FOUND. WEBSITE ERROR

Abstract:

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Paper's Title:

On Automorphisms and Bi-derivations of Semiprime Rings

Author(s):

Abu Zaid Ansari, Faiza Shujat, Ahlam Fallatah

Department of Mathematics,
Faculty of Science,
Islamic University of Madinah, Madinah
K.S.A.
E-mail: ansari.abuzaid@gmail.com, ansari.abuzaid@iu.edu.sa

Department of Mathematics
Faculty of Science
Taibah University, Madinah,
K.S.A.
E-mail: faiza.shujat@gmail.com, fullahkhan@taibahu.edu.sa

Department of Mathematics
Faculty of Science
Taibah University, Madinah,
K.S.A.
E-mail: Afallatah@taibahu.edu.sa
 

Abstract:

In this article, our goal is to figure out a functional equation involving automorphisms and bi-derivations on certain semiprime ring. Also, we characterize the structure of automorphism, in case of prime rings.

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Paper's Title:

Multivalued Equilibrium Problems with Trifunction

Author(s):

Muhammad Aslam Noor

Etisalat College of Engineering, P.O. Box 980, Sharjah, United Arab Emirates
noor@ece.ac.ae

Abstract:

In this paper, we use the auxiliary principle technique to suggest some new classes of iterative algorithms for solving multivalued equilibrium problems with trifunction. The convergence of the proposed methods either requires partially relaxed strongly monotonicity or pseudomonotonicity. As special cases, we obtain a number of known and new results for solving various classes of equilibrium and variational inequality problems. Since multivalued equilibrium problems with trifunction include equilibrium, variational inequality and complementarity problems as specials cases, our results continue to hold for these problems.

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Paper's Title:

A Simple New Proof of Fan-Taussky-Todd Inequalities

Author(s):

Zhi-Hua Zhang and Zhen-Gang Xiao

Zixing Educational Research Section,
Chenzhou City, Hunan 423400, P. R. China.
Zhi-hua Zhang
Url: http://www.hnzxslzx.com/zzhweb/ 

Department Of Mathematics, Hunan Institute Of Science And Technology,
Yueyang City, Hunan 423400, P. R. China.
Zhen-gang Xiao 

Abstract:

In this paper we present simple new proofs of the inequalities:

which holds for all real numbers a₀ = 0, a₁, · · · , a_n, a_n+1 = 0 and the coefficients 2(1 - cos(π/(n + 1))) and 2(1 + cos(π/(n + 1))) are the best possible; and

which holds for all real numbers a₀ = 0, a₁, · · · , a_n and the coefficients 2(1-cos(π/(2n + 1))) and 2(1 + cos(π/(2n + 1))) are the best possible.

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Paper's Title:

Weak Solution for Hyperbolic Equations with a Non-Local Condition

Author(s):

Lazhar Bougoffa

King Khalid University, Faculty of Science, Department of Mathematics,
P.O.Box 9004, Abha, Saudi Arabia
abogafah@kku.edu.sa

 

Abstract:

In this paper, we study hyperbolic equations with a non-local condition. We prove the existence and uniqueness of weak solutions, using energy inequality and the density of the range of the operator generated by the problem.

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Paper's Title:

Weyl Transform Associated With Bessel and Laguerre Functions

Author(s):

E. Jebbari and M . Sifi

Department of Mathematics Faculty of Sciences of Tunis,
1060 Tunis,
Tunisia.
mohamed.sifi@fst.rnu.tn

Abstract:

We define and study the Wigner transform associated to Bessel and Laguerre transform and we prove an inversion formula for this transform. Next we consider a class of symbols which allows to define the Bessel-Laguerre Weyl transform. We establish a relation between the Wigner and Weyl transform. At last, we discuss criterion in term of symbols for the boundedness and compactness of the Bessel-Laguerre Weyl transform.

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Paper's Title:

On Zeros of Diagonally Quasiconvex Multifunctions

Author(s):

Zoran D. Mitrović

Faculty of Electrical Engineering,
University of Banja Luka,
78000 Banja Luka, Patre 5
Bosnia and Herzegovina
zmitrovic@etfbl.net

Abstract:

In this paper, we extended the notion of diagonally quasiconvexity for multifunctions and established several existence results for zeros of diagonally quasiconvex multifunctions. As applications we obtain the results of fixed points, coincidence points and best approximations for multifunctions. Using our result we also prove the existence of solutions to the variational-like inequality problem and generalized vector equilibrium problem. The results of this paper generalize some known results in the literature.

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Paper's Title:

A New Hardy-Hilbert's Type Inequality for Double Series and its Applications

Author(s):

Mingzhe Gao

Department of Mathematics and Computer Science, Normal College Jishou University,
Jishou Hunan, 416000,
People's Republic of China
mingzhegao1940@yahoo.com.cn

Abstract:

In this paper, it is shown that a new Hardy-Hilbert’s type inequality for double series can be established by introducing a parameter and the weight function of the form where c is Euler constant and And the coefficient is proved to be the best possible. And as the mathematics aesthetics, several important constants and appear simultaneously in the coefficient and the weight function when In particular, for case some new Hilbert’s type inequalities are obtained. As applications, some extensions of Hardy-Littlewood’s inequality are given.

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Paper's Title:

Oscillations of First Order Linear Delay Difference Equations

Author(s):

G. E. Chatzarakis and I. P. Stavroulakis

Department of Mathematics, University of Ioannina,
451 10, Greece
ipstav@cc.uoi.gr

Abstract:

Consider the first order linear delay difference equation of the form   where  is a sequence of nonnegative real numbers, k is a positive integer and  denotes the forward difference operator  New oscillation criteria are established when the well-known oscillation conditions  and  are not satisfied. The results obtained essentially improve known results in the literature.

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Paper's Title:

A Stability of the G-type Functional Equation

Author(s):

Gwang Hui Kim

Department of Mathematics, Kangnam University
Suwon 449-702, Korea.
ghkim@kangnam.ac.kr

Abstract:

We will investigate the stability in the sense of Găvruţă for the G-type functional equation f(φ(x))=Γ(x)f(x)+ψ(x) and the stability in the sense of Ger for the functional equation of the form f(φ(x))=Γ(x)f(x). As a consequence, we obtain a stability results for G-function equation.

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Paper's Title:

A note on Inequalities due to Martins, Bennett and Alzer

Author(s):

József Sándor

Babeş-Bolyai University of Cluj, Department of Mathematics and Computer Sciences
Kogălniceanu Nr.1, Cluj-Napoca,
Romania.
jjsandor@hotmail.com
jsandor@member.ams.org

Abstract:

A short history of certain inequalities by Martins, Bennett as well as Alzer, is provided. It is shown that, the inequality of Alzer for negative powers [6], or Martin's reverse inequality [7] are due in fact to Alzer [2]. Some related results, as well as a conjecture, are stated.

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Paper's Title:

Existence of Solutions for Third Order Nonlinear Boundary Value Problems

Author(s):

Yue Hu and Zuodong Yang

School of Mathematics and Computer Science, Nanjing Normal University, Jiangsu Nanjing 210097,
China.
huu3y2@163.com

College of Zhongbei, Nanjing Normal University, Jiangsu Nanjing 210046,
China.
zdyang_jin@263.net
yangzuodong@njnu.edu.cn

Abstract:

In this paper, the existence of solution for a class of third order quasilinear ordinary differential equations with nonlinear boundary value problems

(Φ_p(u"))'=f(t,u,u',u"), u(0)=A, u'(0)=B, R(u'(1),u"(1))=0

is established. The results are obtained by using upper and lower solution methods.

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Paper's Title:

Construction of Lyapunov Functionals In Functional Differential Equations With Applications To Exponential Stability In Volterra Integro-differential Equations

Author(s):

Youssef N. Raffoul

Department of Mathematics, University of Dayton,
Dayton OH 45469-2316,
USA
youssef.raffoul@notes.udayton.edu
URL:http://academic.udayton.edu/YoussefRaffoul

Abstract:

Non-negative definite Lyapunov functionals are employed to obtain sufficient conditions that guarantee the exponential asymptotic stability and uniform exponential asymptotic stability of the zero solution of nonlinear functional differential systems. The theory is applied to Volterra integro-differential equations in the form of proposition examples.

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Paper's Title:

On the Asymptotic Behavior of Solutions of Third Order Nonlinear Differential Equations

Author(s):

Ivan Mojsej and Alena Tartaľová

Institute of Mathematics,
Faculty of Science, P. J. Šafárik University,
Jesenná 5, 041 54 Košice,
Slovak Republic
ivan.mojsej@upjs.sk

Department of Applied Mathematics and Business Informatics,
Faculty of Economics, Technical University,
Nemcovej 32, 040 01 Košice,
Slovak Republic
alena.tartalova@tuke.sk

Abstract:

This paper is concerned with the asymptotic behavior of solutions of nonlinear differential equations of the third order with quasiderivatives. Mainly, we present the necessary and sufficient conditions for the existence of nonoscillatory solutions with specified asymptotic behavior as t tends to infinity. These conditions are presented as integral criteria and involve only the coefficients of investigated differential equations. In order to prove some of the results, we use a topological approach based on the Schauder fixed point theorem.

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Paper's Title:

Equilibria and Periodic Solutions of Projected Dynamical Systems on Sets with Corners

Author(s):

Matthew D. Johnston and Monica-Gabriela Cojocaru

Department of Applied Mathematics, University of Waterloo,
Ontario, Canada
mdjohnst@math.uwaterloo.ca

Department of Mathematics & Statistics, University of Guelph,
Ontario, Canada
mcojocar@uoguelph.ca

Abstract:

Projected dynamical systems theory represents a bridge between the static worlds of variational inequalities and equilibrium problems, and the dynamic world of ordinary differential equations. A projected dynamical system (PDS) is given by the flow of a projected differential equation, an ordinary differential equation whose trajectories are restricted to a constraint set K. Projected differential equations are defined by discontinuous vector fields and so standard differential equations theory cannot apply. The formal study of PDS began in the 90's, although some results existed in the literature since the 70's. In this paper we present a novel result regarding existence of equilibria and periodic cycles of a finite dimensional PDS on constraint sets K, whose points satisfy a corner condition. The novelty is due to proving existence of boundary equilibria without using a variational inequality approach or monotonicity type conditions.

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Paper's Title:

A Subclass of Meromorphically Multivalent Functions with Applications to Generalized Hypergeometric Functions

Author(s):

M. K. Aouf

Mathematics Department, Faculty of Science,
Mansoura University 35516,
Egypt
mkaouf127@yahoo.com

Abstract:

In this paper a new subclass of meromorphically multivalent functions, which is defined by means of a Hadamard product (or convolution) involving some suitably normalized meromorphically p-valent functions. The main object of the present paper is to investigate the various important properties and characteristics of this subclass of meromorphically multivalent functions. We also derive many interesting results for the Hadamard products of functions belonging to this subclass. Also we consider several applications of our main results to generalized hypergeomtric functions.

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Paper's Title:

A Fixed Point Approach to the Stability of the Equation

Author(s):

Soon-Mo Jung

Mathematics Section, College of Science and Technology
 Hong-Ik University, 339-701 Chochiwon
 Republic of Korea.
smjung@hongik.ac.kr

Abstract:

We will apply a fixed point method for proving the Hyers--Ulam stability of the functional equation .

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Paper's Title:

A-Normal Operators In Semi Hilbertian Spaces

Author(s):

A. Saddi

Department of Mathematics,
College of Education for Girls in Sarat Ebeidah 61914, Abha,
King Khalid University
Saudi Arabia
adel.saddi@fsg.rnu.tn
 

Abstract:

In this paper we study some properties and inequalities of A-normal operators in semi-Hilbertian spaces by employing some known results for vectors in inner product spaces. We generalize also most of the inequalities of (α,β)-normal operators discussed in Hilbert spaces [7].

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Paper's Title:

Ellipses Inscribed in Parallelograms

Author(s):

A. Horwitz

Penn State University,
25 Yearsley Mill Rd.
Media, PA 19063
U. S. A. 
alh4@psu.edu
 

Abstract:

We prove that there exists a unique ellipse of minimal eccentricity, E_I, inscribed in a parallelogram, Ð. We also prove that the smallest nonnegative angle between equal conjugate diameters of $E_I equals the smallest nonnegative angle between the diagonals of Ð. We also prove that if E_M is the unique ellipse inscribed in a rectangle, R, which is tangent at the midpoints of the sides of R, then E_M is the unique ellipse of minimal eccentricity, maximal area, and maximal arc length inscribed in R. Let Ð be any convex quadrilateral. In previous papers, the author proved that there is a unique ellipse of minimal eccentricity, E_I, inscribed in Ð, and a unique ellipse, E_O, of minimal eccentricity circumscribed about Ð. We defined Ð to be bielliptic if E_I and E_O have the same eccentricity. In this paper we show that a parallelogram, Ð, is bielliptic if and only if the square of the length of one of the diagonals of Ð equals twice the square of the length of one of the sides of Ð .

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Paper's Title:

Uniform Continuity and k-Convexity

Author(s):

Adel Afif Abdelkarim

Mathematics Department, Faculty of Science, J
erash University, Jerash
Jordan.

adelafifo_afifo@yahoo.com

Abstract:

A closed arcwise-connected subset A of Rⁿ is called k-convex if for each positive number a and for all elements x and y in A there is a positive number b such that if the norm of x-y is less than or equal to b then the length of the shortest curve l(x,y) in A is less than k times the norm of x-y plus a. We show that a union of two non disjoint closed finite convex subsets need not be k-convex. Let f(x) be a uniformly continuous functions on a finite number of closed subsets A_{1},...,A_{n} of R^{n} such that the union of A_{j},...,A_{n},j=1,...,n-1 is k-convex. We show that f is uniformly continuous on the union of the sets A_{i},i=1,...,n. We give counter examples if this condition is not satisfied. As a corollary we show that if f(x) is uniformly continuous on each of two closed convex sets A,B then f(x) is uniformly continuous on the union of A and B.

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Paper's Title:

Renormalized Solutions for Nonlinear Parabolic Equation with Lower Order Terms

Author(s):

A. Aberqi¹, J. Bennouna¹, M. Mekkour¹ and H. Redwane²

¹Université Sidi Mohammed Ben Abdellah,
Département de Mathématiques,
Laboratoire LAMA, Faculté des Sciences Dhar-Mahrez,
B.P 1796 Atlas Fés,
Morocco.

²Faculté des Sciences Juridiques, Economiques et Sociales,
Université Hassan 1, B.P. 784. Settat,
Morocco.

aberqiahmed@ya_hoo.fr
jbennouna@hotmail.com
mekkour.mounir@yahoo.fr
redwane_hicham@yahoo.fr

Abstract:

In this paper, we study the existence of renormalized solutions for the nonlinear parabolic problem: ,where the right side belongs to L¹(Ω×(0,T)) and b(u) is unbounded function of u, the term div(a(x,t,u,∇u)) is a Leray--Lions operator and the function φ is a nonlinear lower order and satisfy only the growth condition.

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Paper's Title:

An Improvement of the Hermite-Hadamard Inequality for Functions Convex on the Coordinates

Author(s):

Milica Klaričić Bakula

Faculty of Science,
University of Split,
Teslina 12, 21000 Split.
Croatia

E-mail: milica@pmfst.hr

Abstract:

An improvement of the Hermite-Hadamard inequality for functions convex on the coordinates is given.

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Paper's Title:

Some Double λ-Convergent Sequence Spaces Over n-Normed Spaces

Author(s):

Kuldip Raj, Renu Anand and Seema Jamwal

School of Mathematics,
Shri Mata Vaishno Devi University Katra-182320,
Jammu and Kashmir,
India.

E-mail: kuldipraj68@gmail.com,  renuanand71@gmail.com, seemajamwal8@gmail.com

Abstract:

In this paper we introduce some double generalized λ-convergent sequence spaces over n-normed spaces defined by Musielak-Orlicz function M = (M_k,l). We also made an attempt to study some topological and algebraic properties of these sequence spaces.

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Paper's Title:

Some Grüss Type Inequalities in Inner Product Spaces

Author(s):

Sever S. Dragomir^1,2

¹Mathematics, School of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au

 
²School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa

URL: http://rgmia.org/dragomir 

Abstract:

Some inequalities in inner product spaces that provide upper bounds for the quantities

and  ,

where e,f ∈ H with and x,y are vectors in H satisfying some appropriate assumptions are given. Applications for discrete and integral inequalities are provided as well.

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Paper's Title:

On Closed Range C^*-modular Operators

Author(s):

Javad Farokhi-Ostad and Ali Reza Janfada

Department of Mathematics,
Faculty of Mathematics and Statistics Sciences,
University of Birjand, Birjand,
Iran.
E-mail: j.farokhi@birjand.ac.ir ajanfada@birjand.ac.ir

Abstract:

In this paper, for the class of the modular operators on Hilbert C^*-modules, we give the conditions to closedness of their ranges. Also, the equivalence conditions for the closedness of the range of the modular projections on Hilbert C^*-modules are discussed. Moreover, the mixed reverse order law for the Moore-Penrose invertible modular operators are given.

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Paper's Title:

Existence of Optimal Parameters for Damped Sine-Gordon Equation with Variable Diffusion Coefficient and Neumann Boundary Conditions

Author(s):

N. Thapa

Department of Mathematical Sciences,
Cameron University,
2800 West Gore Blvd,
73505 Lawton, Oklahoma,
USA.
E-mail: nthapa@cameron.edu
URL: http://www.cameron.edu/~nthapa/

Abstract:

The parameter identification problem for sine-Gordon equation is of a major interests among mathematicians and scientists.\ In this work we the consider sine-Gordon equation with variable diffusion coefficient and Neumann boundary data. We show the existence and uniqueness of weak solution for sine-Gordon equation. Then we show that the weak solution continuously depends on parameters. Finally we show the existence of optimal set of parameters.

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Paper's Title:

On a New Class of Eulerian's Type Integrals Involving Generalized Hypergeometric Functions

Author(s):

Sungtae Jun, Insuk Kim and Arjun K. Rathie

General Education Institute,
Konkuk University, Chungju 380-701,
Republic of Korea.

Department of Mathematics Education,
Wonkwang University, Iksan, 570-749,
Republic of Korea.

Department of Mathematics,
Vedant College of Engineering and Technology (Rajasthan Technical University),
Bundi-323021, Rajasthan,
India.

E-mail: sjun@kku.ac.kr, iki@wku.ac.kr, arjunkumarrathie@gmail.com

Abstract:

Very recently Masjed-Jamei and Koepf established interesting and useful generalizations of various classical summation theorems for the ₂F₁, ₃F₂, ₄F₃, ₅F₄ and ₆F₅ generalized hypergeometric series. The main aim of this paper is to establish eleven Eulerian's type integrals involving generalized hypergeometric functions by employing these theorems. Several special cases have also been given.

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Paper's Title:

Weyl's theorem for class Q and k - quasi class Q Operators

Author(s):

S. Parvatham and D. Senthilkumar

Department of Mathematics and Humanities,
Sri Ramakrishna Institute of Technology, Coimbatore-10, Tamilnadu,
India.
E-mail: parvathasathish@gmail.com

Post Graduate and Research Department of Mathematics,
Govt. Arts College, Coimbatore-641018, Tamilnadu,
India.
E-mail: senthilsenkumhari@gmail.com

Abstract:

In this paper, we give some properties of class  Q  operators. It is proved that every class  Q  operators satisfies Weyl's theorem under the condition that  T²  is isometry. Also we proved that every  k  quasi class  Q  operators is Polaroid and the spectral mapping theorem holds for this class of operator. It will be proved that single valued extension property, Weyl and generalized Weyl's theorem holds for every  k  quasi class  Q  operators.

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Paper's Title:

Double Difference of Composition Operator on Bloch Spaces

Author(s):

Rinchen Tundup

Department of Mathematics
University of Jammu
Jammu and Kashmir
India.

E-mail: joneytun123@gmail.com

Abstract:

In this paper we characterize the compactness of double difference of three non-compact composition operators on Bloch space induced by three holomorphic self maps on the unit disc.

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Paper's Title:

Evaluation of a New Class of Double Integrals Involving Generalized Hypergeometric Function ₄F₃

Author(s):

Joohyung Kim, Insuk Kim and Harsh V. Harsh

Department of Mathematics Education,
Wonkwang University, Iksan, 570-749,
Korea.
E-mail: joohyung@wku.ac.kr
 
Department of Mathematics Education,
Wonkwang University, Iksan, 570-749,
Korea.
E-mail: iki@wku.ac.kr

Department of Mathematics, Amity School of Eng. and Tech.,
Amity University Rajasthan
NH-11C, Jaipur-303002, Rajasthan,
India.
E-mail: harshvardhanharsh@gmail.com

Abstract:

Very recently, Kim evaluated some double integrals involving a generalized hypergeometric function ₃F₂ with the help of generalization of Edwards's well-known double integral due to Kim,  et al. and generalized classical Watson's summation theorem obtained earlier by Lavoie,  et al. In this research paper we evaluate one hundred double integrals involving generalized hypergeometric function ₄F₃ in the form of four master formulas (25 each) viz. in the most general form for any integer. Some interesting results have also be obtained as special cases of our main findings.

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Paper's Title:

Oscillatory Behavior of Second-Order Non-Canonical Retarded Difference Equations

Author(s):

G.E. Chatzarakis¹, N. Indrajith², E. Thandapani³ and K.S. Vidhyaa⁴

¹Department of Electrical and Electronic Engineering Educators,
School of Pedagogical and Technological Education,
Marousi 15122, Athens,
Greece.
E-mail:  gea.xatz@aspete.gr, geaxatz@otenet.gr
 

²Department of Mathematics,
Presidency College, Chennai - 600 005,
India.
E-mail: indrajithna@gmail.com

³Ramanujan Institute for Advanced Study in Mathematics,
University of Madras,
Chennai - 600 005,
India.
E-mail: ethandapani@yahoo.co.in

⁴Department of Mathematics,
SRM Easwari Engineering College,
Chennai-600089,
India.
E-mail: vidyacertain@gmail.com

Abstract:

Using monotonic properties of nonoscillatory solutions, we obtain new oscillatory criteria for the second-order non-canonical difference equation with retarded argument

Our oscillation results improve and extend the earlier ones. Examples illustrating the results are provided.

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Paper's Title:

Improved Oscillation Criteria of Second-Order Advanced Non-canonical Difference Equation

Author(s):

G. E. Chatzarakis¹, N. Indrajith², S. L. Panetsos¹, E. Thandapani³

¹Department of Electrical and Electronic Engineering Educators
School of Pedagogical and Technological Education,
Marousi 15122, Athens,
Greece.
E-mail: gea.xatz@aspete.gr, geaxatz@otenet.gr
spanetsos@aspete.gr

²Department of Mathematics,
Presidency College, Chennai - 600 005,
India.
E-mail: indrajithna@gmail.com

³Ramanujan Institute for Advanced Study in Mathematics,
University of Madras Chennai - 600 005,
India.
E-mail: ethandapani@yahoo.co.in

Abstract:

Employing monotonic properties of nonoscillatory solutions, we derive some new oscillation criteria for the second-order advanced non-canonical difference equation

Our results extend and improve the earlier ones. The outcome is illustrated via some particular difference equations.

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Paper's Title:

Corrigendum for Multistage Analytical Approximate Solution of Quasi-Linear Differential- Algebraic System of Index Two

Author(s):

Ibrahim M. Albak, F. A. Abdullah^* and Zarita Zainuddin

School of Mathematical Sciences,
 Universiti Sains Malaysia,
 11800 USM, Penang,
Malaysia.
E-mail:  ibra13975@gmail.com,
farahaini@usm.my,
zarita@usm.my

Abstract:

This article is a corrigendum to AJMAA Volume 18, Issue 2, Article 13, {PDF Link}.

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Paper's Title:

Fekete-Szegö Inequality for Sakaguchi Type of functions in Petal Shaped Domain

Author(s):

E. K. Nithiyanandham and B. Srutha Keerthi

Division of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology Chennai Campus,
Chennai - 600 048,
India.
E-mail: nithiyankrish@gmail.com

Division of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology Chennai Campus,
Chennai - 600 048,
India.
E-mail: keerthivitmaths@gmail.com

Abstract:

In this paper, we estimate coefficient bounds,|a_2|,|a_3| and |a_4|, Fekete-Szegö inequality and Toeplitz determinant T₂(2) and T₃(1) for functions belonging to the following class

 

the function being holomorphic, we expand using Taylor series and obtain several corollaries and consequences for the main result.

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Paper's Title:

Toeplitz Determinant for Sakaguchi Type Functions Under Petal Shaped Domain

Author(s):

B. Nandhini and B. Srutha Keerthi

Division of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology Chennai Campus,
Chennai - 600 048,
India.
E-mail: nandhinibaskar1996@gmail.com

Division of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology Chennai Campus,
Chennai - 600 048,
India.
E-mail: keerthivitmaths@gmail.com

Abstract:

We introduce a new general subclass GP^t,ρ of Sakaguchi kind function on a Petal shaped domain. We obtain coefficients bounds and upper bounds for the Fekete-Szegö functional over the class. From these functions we obtain the bounds of first four coefficients, and then we have derived the Toeplitz determinant T₂(2) and T₃(1) whose diagonal entries are the coefficients of functions.

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Paper's Title:

Metric Functionals for the Hästö Metric

Author(s):

G. Bettencourt and S. Mendes

Departamento de Matemática,
Universidade da Beira Interior -
Covilhã Portugal,
Centro de Matemática e Aplicações
Universidade da Beira Interior -
Covilhã Portugal.
E-mail: gastao@ubi.pt

 
ISCTE - University Institute of Lisbon - Lisbon Portugal,
Centro de Matemática e Aplicações
Universidade da Beira Interior -
Covilhã Portugal.
E-mail: sergio.mendes@iscte-iul.pt

Abstract:

In 2002, new classes of weighted metrics on Rⁿ were introduced by Peter Hästö. In this article we compute the metric functionals for such classes of metrics.

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Paper's Title:

A Determinantal Representation of Core EP Inverse

Author(s):

Divya Shenoy Purushothama

Department of Mathematics,
Manipal Institute of Technology,
Manipal Academy of Higher Education,
Manipal -576104, Karnataka,
India.
E-mail:  divya.shenoy@manipal.edu
URL: https://manipal.edu/mit/department-faculty/faculty-list/divya-shenoy-p.html

Abstract:

The notion of Core EP inverse is introduced by Prasad in the article "Core - EP inverse" and proved its existence and uniqueness. Also, a formula for computing the Core EP inverse is obtained from particular linear combination of minors of a given matrix. Here a determinantal representation for Core EP inverse of a matrix A with the help of rank factorization of A is obtained.

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Paper's Title:

Topological Aspects of Discrete Switch Dynamical Systems

Author(s):

Faiz Imam and Sharan Gopal

Department of Mathematics,
BITS - Pilani, Hyderabad Campus,
India.
E-mail: mefaizy@gmail.com

Department of Mathematics,
BITS - Pilani, Hyderabad Campus,
India.
E-mail: sharanraghu@gmail.com

ABSTRACT NOT FOUND. WEBSITE ERROR

Abstract:

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Paper's Title:

On Some Nonlinear Retarded Integrodifferential Inequalities in Two and n Independent Variables and their Applications

Author(s):

Bitat Dalila and Khellaf Hassane

Department of Mathematics, Laboratory of Applied Mathematics and Modeling,
University of Constantine,
PO Box 325, Ain El Bey Road, Constantine 25017,
Algeria.
E-mail: bitat.dalila@umc.edu.dz khellafhassane@umc.edu.dz
URL: https://www.umc.edu.dz

Abstract:

In this paper, we establish some new nonlinear retarded integrodifferential inequalities in two and n independent variables. Some applications are given as illustration.

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Paper's Title:

Optimal Conditions using Multi-valued G-Presic type Mapping

Author(s):

Deb Sarkar, Ramakant Bhardwaj, Vandana Rathore, and Pulak Konar

Department of Mathematics, Amity
University, Kadampukur, 24PGS(N), Kolkata, West Bengal, 700135,
India.
E-mail: debsarkar1996@gmail.com

Department of Mathematics, Amity
University, Kadampukur, 24PGS(N), Kolkata, West Bengal, 700135,
India.
E-mail: drrkbhardwaj100@gmail.com

School of Engineering and Technology,
Jagran Lakecity University, Bhopal, MP-462044,
India.
E-mail: drvandana@jlu.edu.in

Department of Mathematics,
VIT University, Chennai, Tamil Nadu-600127,
India.
E-mail: pulakkonar@gmail.com

Abstract:

In the present paper, some best proximity results have been presented using the concept of G-Presic type multi-valued mapping. These results are the extensions of Presic's theorem in the non-self mapping. A suitable example has also been given. Here, some applications are presented in θ-chainable space and ordered metric space.

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Paper's Title:

Growth and Approximation of Entire Solutions of Linear Partial Differential Equation in Terms of Bessel Polynomial Approximation Errors in Lp-norm, 1 ≤ p ≤ ∞

Author(s):

Devendra Kumar

Department of Mathematics, Faculty of Sciences
Al-Baha University,
P.O.Box-7738 Alaqiq, Al-Baha-65799,
Saudi Arabia.
E-mail: d_kumar001@rediffmail.com, dsingh@bu.edu.sa

Abstract:

We deal with entire solutions of some special type linear homogeneous partial differential equations that are represented in convergent series of Bessel polynomials. We determine the growth orders and types of the solutions, in terms of Bessel polynomial approximation errors in both sup norm and L^p-norm, 1 ≤ p ≤ ∞.

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Paper's Title:

On Sufficient Conditions for Strong Starlikeness

Author(s):

V. Ravichandran, M. H. Khan, M. Darus, And K. G. Subramanian

School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Usm Penang, Malaysia
vravi@cs.usm.my
Url: http://cs.usm.my/~vravi/index.html

Department of Mathematics, Islamiah College, Vaniambadi 635 751, India
khanhussaff@yahoo.co.in

School of Mathematical Sciences, Faculty of Science and Technology, UKM, Bangi 43600,
Malaysia
maslina@pkrisc.cc.ukm.my
Url: http://www.webspawner.com/users/maslinadarus

Department of Mathematics, Madras Christian College, Tambaram, Chennai 600 059, India
kgsmani@vsnl.net

Abstract:

In the present investigation, we obtain some sufficient conditions for a normalized analytic function f(z) defined on the unit disk to satisfy the condition

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Paper's Title:

Generalized Fuglede-Putnam Theorem and Orthogonality

Author(s):

A. Bachir and A. Sagres

Department of Mathematics, Faculty of Science, King Khaled University, Abha, P.O. Box 9004 Kingdom Saudi Arabia
bachir_ahmed@hotmail.com
sagres@hotmail.com

Abstract:

An asymmetric Fuglede-Putnam’s theorem for dominant operators and p-hyponormal operators is proved, as a consequence of this result, we obtain that the range of the generalized derivation induced by the above classes of operators is orthogonal to its kernel.

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Paper's Title:

On Certain Classes of Harmonic Univalent Functions Based on Salagean Operator

Author(s):

G. Murugusundaramoorthy, Thomas Rosy, and B. A. Stephen

Department of Applied Mathematics and Informatics,
Department of Mathematics, Vellore Institute of Technology,
Deemed University, Vellore - 632014, India.
gmsmoorthy@yahoo.com 

Department of Applied Mathematics and Informatics,
Department of Mathematics, Madras Christian College,
Chennai - 600059, India.
drthomasrosy@rediffmail.com 

Abstract:

We define and investigate a class of complex-valued harmonic univalent functions of the form f = h + g using Salagean operator where h and g are analytic in the unit disc U = { z : |z| < 1 }. A necessary and sufficient coefficient conditions are given for functions in these classes. Furthermore, distortion theorems, inclusion relations, extreme points, convolution conditions and convex combinations for this family of harmonic functions are obtained.

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Paper's Title:

Ellipses of Maximal Area and of Minimal Eccentricity Inscribed in a Convex Quadrilateral

Author(s):

Alan Horwitz

Penn State University,
25 Yearsley Mill Rd., Media, Pa 19063
alh4@psu.edu 
Url: www.math.psu.edu/horwitz

Abstract:

Let Ð be a convex quadrilateral in the plane and let M1 and M2 be the midpoints of the diagonals of Ð. It is well–known that if E is an ellipse inscribed in Ð, then the center of E must lie on Z, the open line segment connecting M1 and M2 . We use a theorem of Marden relating the foci of an ellipse tangent to the lines thru the sides of a triangle and the zeros of a partial fraction expansion to prove the converse: If P lies on Z, then there is a unique ellipse with center P inscribed in Ð. This completely characterizes the locus of centers of ellipses inscribed in Ð. We also show that there is a unique ellipse of maximal area inscribed in Ð. Finally, we prove our most signifigant results: There is a unique ellipse of minimal eccentricity inscribed in Ð.

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Paper's Title:

New Coincidence and Fixed Point Theorems for Strictly Contractive Hybrid Maps

Author(s):

S. L. Singh and Amal M. Hashim

21, Govind Nagar, Rishikesh 249201,
Ua, India
vedicmri@sancharnet.in

Dept. of Math., College of Science,
Univ. of Basarah,
Iraq.
 

Abstract:

The purpose of this paper is to study the (EA)-property and noncompatible maps of a hybrid pair of single-valued and multivalued maps in fixed point considerations. Such maps have the remarkable property that they need not be continuous at their common fixed points. We use this property to obtain some coincidence and fixed point theorems for strictly contractive hybrid maps without using their continuity and completeness or compactness of the space.

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Paper's Title:

Quantitative Estimates for Positive Linear Operators Obtained by Means of Piecewise Linear Functions

Author(s):

Vasile Mihesan

Technical University of Cluj-Napoca,
Department of Mathematics,
Str. C. Daicoviciu 15, Cluj-Napoca,
Romania
Vasile.Mihesan@math.utcluj.ro

 

Abstract:

In this paper we obtain estimates for the remainder in approximating continuous functions by positive linear operators, using piecewise linear functions.

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Paper's Title:

Stability of a Pexiderized Equation

Author(s):

Maryam Amyar

Department of Mathematics,
Islamic Azad University, Rahnamaei Ave,
Mashhad 91735, Iran,
and Banach Mathematical Research Group (BMRG)
amyari@mshdiau.ac.ir

URL: http://amyari.mshdiau.ac.ir

Abstract:

The aim of the paper is to prove the stability of the Pexiderized equation f(x)=g(y+x)-h(y-x), for any amenable abelian group.

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Paper's Title:

Notes on Sakaguchi Functions

Author(s):

Shigeyoshi Owa, Tadayuki Sekine and Rikuo Yamakawa

Department of Mathematics, Kinki University,
Higashi-Osaka, Osaka 577-8502,
Japan.
owa@math.kindai.ac.jp

Office of Mathematics, College of Pharmacy, Nihon University,
7-1 Narashinodai, Funabashi-city,
Chiba, 274-8555, Japan.
tsekine@pha.nihon-u.ac.jp

Department of Mathematics, Shibaura Institute of Technology,
Minuma, Saitama-city,
Saitama 337-8570, Japan.
yamakawa@sic.shibaura-it.ac.jp

Abstract:

By using the definition for certain univalent functions f(z) in the open unit disk U given by K. Sakaguchi [2], two classes S(α) and T(α) of analytic functions in U are introduced. The object of the present paper is to discuss some properties of functions f(z) belonging to the classes S(α) and T(α).

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Paper's Title:

Existence of Non-spurious Solutions to Discrete Boundary Value Problems

Author(s):

Irena Rachunkova and Christopher C. Tisdell

Department of Mathematics
Palacky University
771 46 Olomouc, Czech Republic.
rachunko@risc.upol.cz
URL: http://phoenix.inf.upol.cz/~rachunekl/mathair/matha-en.htm

School of Mathematics
The University of New South Wales
Sydney 2052, Australia.
cct@unsw.edu.au
URL: http://www.maths.unsw.edu.au/~cct

Abstract:

This paper investigates discrete boundary value problems (BVPs) involving second-order difference equations and two-point boundary conditions. General theorems guaranteeing the existence and uniqueness of solutions to the discrete BVP are established. The methods involve a sufficient growth condition to yield an a priori bound on solutions to a certain family of discrete BVPs. The em a priori bounds on solutions to the discrete BVP do not depend on the step-size and thus there are no ``spurious'' solutions. It is shown that solutions of the discrete BVP will converge to solutions of ordinary differential equations.

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Paper's Title:

Generalized Quasilinearization Method for the Forced Düffing Equation

Author(s):

Ramzi S. N. Alsaedi

Department of Mathematics, King Abdul Aziz University,
Jeddah P.O. Box 80203,
Saudi Arabia.
ramzialsaedi@yahoo.co.uk

Abstract:

A generalized quasilinearization method for the periodic problem related to the forced D\"{u}ffing equation is developed and a sequence of approximate solutions converging monotonically and quadratically to the solution of the given problem is presented.

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Paper's Title:

On the Generalized Inverse over Integral Domains

Author(s):

Yaoming Yu and Guorong Wang

College of Education, Shanghai Normal University
Shanghai 200234
People's Republic of China.
yuyaoming@online.sh.cn
grwang@shnu.edu.cn

Abstract:

In this paper, we study further the generalized inverse of a matrix A over an integral domain. We give firstly some necessary and sufficient conditions for the existence of the generalized inverse , an explicit expression for the elements of the generalized inverse and an explicit expression for the generalized inverse , which reduces to the {1} inverse. Secondly, we verify that the group inverse, the Drazin inverse, the Moore-Penrose inverse and the weighted Moore-Penrose inverse are identical with the generalized inverse for an appropriate matrix G, respectively, and then we unify the conditions for the existence and the expression for the elements of the weighted Moore-Penrose inverse, the Moore-Penrose inverse, the Drazin inverse and the group inverse over an integral domain. Thirdly, as a simple application, we give the relation between some rank equation and the existence of the generalized inverse , and a method to compute the generalized inverse . Finally, we give an example of evaluating the elements of without calculating .

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Paper's Title:

Power and Euler-Lagrange Norms

Author(s):

Mohammad Sal Moslehian and John Michael Rassias

Department of Mathematics,
Ferdowsi University,
P. O. Box 1159, Mashhad 91775,
Iran;
Department of Pure Mathematics,
University of Leeds,
Leeds LS2 9JT,
United Kingdom.
moslehian@ferdowsi.um.ac.ir
URL: http://www.um.ac.ir/~moslehian/

Pedagogical Department, E.E., Section of Mathematics and Informatics
National and Capodistrian University of Athens,
4, Agamemnonos str., Aghia Paraskevi, Attikis 15342, Athens,
Greece.
jrassias@primedu.uoa.gr
URL: http://www.primedu.uoa.gr/~jrassias/

Abstract:

We introduce the notions of power and Euler-Lagrange norms by replacing the triangle inequality, in the definition of norm, by appropriate inequalities. We prove that every usual norm is a power norm and vice versa. We also show that every norm is an Euler-Lagrange norm and that the converse is true under certain condition.

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Paper's Title:

Two Classes of Completely Monotonic Functions Involving Gamma and Polygamma Functions

Author(s):

Bai-Ni Guo, Xiao-Ai Li and Feng Qi

School of Mathematics and Informatics, Henan Polytechnic University,
Jiaozuo City, Henan Province, 454010,
China.
bai.ni.guo@gmail.com

College of Mathematics and Information Science,
Henan Normal University, Xinxiang City,
Henan Province, 453007,
China.
lxa.hnsd@163.com

Research Institute of Mathematical Inequality Theory,
Henan Polytechnic University, Jiaozuo City,
Henan Province, 454010,
China
qifeng618@gmail.com
qifeng618@hotmail.com
qifeng618@qq.com
URLhttp://rgmia.vu.edu.au/qi.html

Abstract:

The function

is logarithmically completely monotonic in (0,∞) if and only if c≥1 and its reciprocal is logarithmically completely monotonic in (0,∞) if and only if c≤0. The function

is completely monotonic in (0,∞) if and only if c≥1 and its negative is completely monotonic in (0,∞)  if and only if c≤0.

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Paper's Title:

The Invariant Subspace Problem for Linear Relations on Hilbert Spaces

Author(s):

Daniel Grixti-Cheng

Department of Mathematics and Statistics,
The University of Melbourne,
Melbourne, VIC, 3010
Australia.
D.Grixti@ms.unimelb.edu.au

Abstract:

We consider the invariant subspace problem for linear relations on Hilbert spaces with the aim of promoting interest in the problem as viewed from the theory of linear relations. We present an equivalence between the single valued and multivalued invariant subspace problems and give some new theorems pertaining to the invariant subspace problem for linear relations on a Hilbert space.

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Paper's Title:

A Method for Solving Systems of Nonlinear Equations

Author(s):

J. Shokri

Department of Mathematics, Urmia University,
P. O. Box 165, Urmia,
Iran
j.shokri@urmia.ac.ir

Abstract:

In this paper, we suggest and analyze a new two-step iterative method for solving nonlinear equation systems using the combination of midpoint quadrature rule and Trapezoidal quadrature rule. We prove that this method has quadratic convergence. Several examples are given to illustrate the efficiency of the proposed method.

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Paper's Title:

The Riemann-Stieltjes Integral on Time Scales

Author(s):

D. Mozyrska, E. Pawłuszewicz, D. Torres

Faculty Of Computer Science,
Białystok University Of Technology,
15-351 Białystok,
 Poland
 d.mozyrska@pb.edu.pl

 Department Of Mathematics,
University Of Aveiro,
3810-193 Aveiro,
Portugal
 ewa@ua.pt

 Department Of Mathematics,
University Of Aveiro,
3810-193 Aveiro,
Portugal
 delfim@ua.pt

 

Abstract:

We study the process of integration on time scales in the sense of Riemann-Stieltjes. Analogues of the classical properties are proved for a generic time scale, and examples are given

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Paper's Title:

Properties of Certain Multivalent Functions Involving Ruscheweyh Derivatives

Author(s):

N-Eng Xu and Ding-Gong Yang

Department of Mathematics,
Changshu Institute of Technology,
Changshu, Jiangsu 215500,
China

xun@cslg.edu.cn
 

Abstract:

Let A_p(p∈ N) be the class of functions which are analytic in the unit disk. By virtue of the Ruscheweyh derivatives we introduce the new subclasses C_p(n,α,β,λ,μ) of A_p. Subordination relations, inclusion relations, convolution properties and a sharp coefficient estimate are obtained. We also give a sufficient condition for a function to be in C_p(n,α,β,λ,μ)

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Paper's Title:

C^*-algebras Associated Noncommutative Circle and Their K-theory

Author(s):

Saleh Omran

Taif University,
Faculty of Science,
Taif,
KSA

South Valley University,
Faculty of Science,
Math. Dep.
Qena,
Egypt

salehomran@yahoo.com

Abstract:

In this article we investigate the universal C^*-algebras associated to certain 1 - dimensional simplicial flag complexes which describe the noncommutative circle. We denote it by S₁^nc. We examine the K-theory of this algebra and the subalgebras S₁^nc/I_k, I_k . Where I_k, for each k, is the ideal in S₁^nc generated by all products of generators h_s containing at least k+1 pairwise different generators. Moreover we prove that such algebra divided by the ideal I₂ is commutative.

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Paper's Title:

Some Applications of Fejér's Inequality for Convex Functions (I)

Author(s):

S.S. Dragomir^1,2 and I. Gomm¹

¹Mathematics, School of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia.

sever.dragomir@vu.edu.au

URL: http://rgmia.org/dragomir

²School of Computational & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa.

Abstract:

Some applications of Fejér's inequality for convex functions are explored. Upper and lower bounds for the weighted integral

under various assumptions for f with applications to the trapezoidal quadrature rule are given. Some inequalities for special means are also provided

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Paper's Title:

Some Operator Order Inequalities for Continuous Functions of Selfadjoint Operators in Hilbert Spaces

Author(s):

S. S. Dragomir^1,2 and Charles E. M. Pearce³

¹Mathematics, School of Engineering & Science,
Victoria University,
PO Box 14428, Melbourne City, MC 8001,
Australia.

²School of Computational & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa.

sever.dragomir@vu.edu.au 
URL: http://rgmia.org/dragomir

³School of Mathematical Sciences,
The University of Adelaide,
Adelaide,
Australia
 

Abstract:

Various bounds in the operator order for the following operator transform

where A is a selfadjoint operator in the Hilbert space H with the spectrum Sp( A) ⊆ [ m,M] and f:[m,M] ->  C is a continuous function on [m,M]  are given. Applications for the power and logarithmic functions are provided as well.

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Paper's Title:

End-Point and Transversality Conditions in the Calculus of Variations: Derivations through Direct Reasoning

Author(s):

Olivier de La Grandville

Stanford University,
Department of Management Science and Engineering,
475 Via Ortega, Stanford, CA 94305,
U. S. A.

E-mail: ola@stanford.edu

Abstract:

We offer an intuitive explanation of the end-point and transversality conditions that complement the Euler equation in the calculus of variations. Our reasoning is based upon the fact that any variation given to an optimal function must entail a zero net gain to the functional, all consequences of implied changes in its derivative being fully taken into account.

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Paper's Title:

Examples of Fractals Satisfying the Quasihyperbolic Boundary Condition

Author(s):

Petteri Harjulehto and Riku Klén

Department of Mathematics and Statistics,
FI-20014 University of Turku,
Finland

E-mail: petteri.harjulehto@utu.fi

E-mail: riku.klen@utu.fi

Abstract:

In this paper we give explicit examples of bounded domains that satisfy the quasihyperbolic boundary condition and calculate the values for the constants. These domains are also John domains and we calculate John constants as well. The authors do not know any other paper where exact values of parameters has been estimated.

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Paper's Title:

On a Class of Meromorphic Functions of Janowski Type Related with a Convolution Operator

Author(s):

Abdul Rahman S. Juma, Husamaldin I. Dhayea

Department of Mathematics,
Alanbar University, Ramadi,
Iraq.
E-mail: dr_juma@hotmail.com

Department of Mathematics,
Tikrit University, Tikrit,
Iraq.
URL: husamaddin@gmail.com

Abstract:

In this paper, we have introduced and studied new operator $Q^k_λ,m,γ by the Hadamard product (or convolution) of two linear operators D^k_λ and I_m,γ, then using this operator to study and investigate a new subclass of meromorphic functions of Janowski type, giving the coefficient bounds, a sufficient condition for a function to belong to the considered class and also a convolution property. The results presented provide generalizations of results given in earlier works.

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Paper's Title:

Hermite-Hadamard Type Inequalities for k-Riemann Liouville Fractional Integrals Via Two Kinds of Convexity

Author(s):

R. Hussain¹, A. Ali², G. Gulshan³, A. Latif⁴ and K. Rauf⁵

^1,2,3,4Department of Mathematics,
Mirpur University of Science and Technology, Mirpur.
Pakistan.
E-mail¹:  rashida12@gmail.com
E-mail²: unigraz2009@yahoo.com
E-mail³: ghazalagulshan@yahoo.com
E-mail⁴: asialatif87@gmail.com

⁵Department of Mathematics,
University of Ilorin, Ilorin,
Nigeria.
E-mail⁵: krauf@unilorin.edu.ng

Abstract:

In this article, a fundamental integral identity including the first order derivative of a given function via k-Riemann-Liouville fractional integral is established. This is used to obtain further Hermite-Hadamard type inequalities involving left-sided and right-sided k-Riemann-Liouville fractional integrals for m-convex and (s,m)-convex functions respectively.

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Paper's Title:

A Note on Divergent Fourier Series and λ-Permutations

Author(s):

A. Castillo, J. Chavez and H. Kim

Tufts University,
Department of Mathematics,
Medford, MA 02155,
USA
E-mail: angel.castillo@tufts.edu

Texas Tech University,
Department of Mathematics and Statistics,
Lubbock, TX 79409,
USA
E-mail: josechavez5@my.unt.edu

University of Michigan-Dearborn,
Department of Mathematics and Statistics,
Dearborn, MI 48128,
USA.
E-mail: khyejin@umich.edu

Abstract:

We present a continuous function on [-π,π] whose Fourier series diverges and it cannot be rearranged to converge by a λ-permutation.

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Paper's Title:

Euler-Maclaurin Formulas for Functions of Bounded Variation

Author(s):

G. De Marco, M. De Zotti, C. Mariconda

Dipartimento di Matematica Tullio Levi-Civita,
Universita degli Studi di Padova
Via Trieste 63, Padova 35121,
Italy.
E-mail:  carlo.mariconda@unipd.it
URL: http://www.math.unipd.it

Abstract:

The first-order Euler-Maclaurin formula relates the sum of the values of a smooth function on an interval of integers with its integral on the same interval on R. We formulate here the analogue for functions that are just of bounded variation.

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Paper's Title:

Kinematic Model for Magnetic Null-points in 2 Dimensions

Author(s):

Ali Khalaf Hussain Al-Hachami

Department of Mathematics,
College of Education For Pure Sciences,
Wasit University,
Iraq.
E-mail: alhachamia@uowasit.edu.iq

Abstract:

The adjacent configurations of two-dimensional magnetic null point centers are analyzed by an immediate examination about the null. The configurations are classified as either potential or non-potential. By then the non-potential cases are subdivided into three cases depending upon whether the component of current is less than, equal to or greater than a threshold current. In addition the essential structure of reconnection in 2D is examined. It unfolds that the manner by which the magnetic flux is rebuilt. In this paper, we center on the ramifications of kinematic arrangements; that is, we fathom just Maxwell's conditions and a resistive Ohm's law.

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Paper's Title:

On The Degree of Approximation of Periodic Functions from Lipschitz and Those from Generalized Lipschitz Classes

Author(s):

Xhevat Z. Krasniqi

Faculty of Education,
University of Prishtina "Hasan Prishtina",
Avenue "Mother Theresa " no. 5, Prishtinë 10000,
Republic of Kosovo.
E-mail: xhevat.krasniqi@uni-pr.edu

Abstract:

In this paper we have introduced some new trigonometric polynomials. Using these polynomials, we have proved some theorems which determine the degree of approximation of periodic functions by a product of two special means of their Fourier series and the conjugate Fourier series. Many results proved previously by others are special case of ours.

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Paper's Title:

Some Properties on a Class of p-valent Functions Involving Generalized Differential Operator

Author(s):

A. T. Yousef, Z. Salleh and T. Al-Hawary

Department of Mathematics,
Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu,
21030 Kuala Nerus, Terengganu,
Malaysia.
E-mail: abduljabaryousef@gmail.com, zabidin@umt.edu.my

 
Department of Applied Science,
Ajloun College, Al-Balqa Applied University,
Ajloun 26816,
Jordan.
E-mail: tariq_amh@yahoo.com

Abstract:

This paper aiming to introduce a new differential operator in the open unit disc We then, introduce a new subclass of analytic function Moreover, we discuss coefficient estimates, growth and distortion theorems, and inclusion properties for the functions belonging to the class

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Paper's Title:

Error Bounds for Numerical Integration of Functions of Lower Smoothness and Gauss-Legendre Quadrature Rule

Author(s):

Samuel A. Surulere and Abiola O. Oladeji

Tshwane University of Technology
Department of Mathematics and Statistics
175, Nelson Mandela drive, Arcadia, Pretoria,
South Africa.
E-mail: samuel.abayomi.sas@gmail.com

Abstract:

The error bounds of the rectangular, trapezoidal and Simpson's rules which are commonly used in approximating the integral of a function (f(x)) over an interval ([a,b]) were estimated. The error bounds of the second, and third generating functions of the Gauss-Legendre quadrature rules were also estimated in this paper. It was shown that for an (f(t)) whose smoothness is increasing, the accuracy of the fourth, sixth and eighth error bound of the second, and third generating functions of the Gauss-Legendre quadrature rule does not increase. It was also shown that the accuracy of the fourth error bound of the Simpson's (1/3) and (3/8) rules does not increase.

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Paper's Title:

Timelike Surfaces with a Common Line of Curvature in Minkowski 3-Space

Author(s):

M.K. Saad, A.Z. Ansari, M. Akram and F. Alharbi

Department of Mathematics ,
Faculty of Science,
Islamic University of Madinah,
KSA

Abstract:

In this paper, we analyze the problem of constructing a timelike surface family from a given non-null curve line of curvature. Using the Frenet frame of the non-null curve in Minkowski space E₁³  we express the family of surfaces as a linear combination of the components of this frame, and derive the necessary and sufficient conditions for the coefficients to satisfy both the line of curvature and the isoparametric requirements. In addition, a necessary and sufficient condition for the given non-null curve to satisfy the line of curvature and the geodesic requirements is investigated. The extension to timelike surfaces of revolution is also outlined. Meanwhile, some representative non-null curves are chosen to construct the corresponding timelike surfaces which possessing these curves as lines of curvature. Results presented in this paper have applications in geometric modeling and the manufacturing of products. In addition, some computational examples are given and plotted.

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Paper's Title:

Coefficient Bounds for Sakaguchi Kind of Functions Associated with Sine Function

Author(s):

Serap Bulut, H. Priya and B. Srutha Keerth

Kocaeli University,
Faculty of Aviation and Space Sciences,
Arslanbey Campus, 41285 Kartepe-Kocaeli,
Turkey.
E-mail: serap.bulut@kocaeli.edu.tr

 
Department of Mathematics,
School of Advanced Sciences,
VIT Chennai Campus, Chennai - 600 048,
India.
E-mail: priyaharikrishnan18@gmail.com, priya.h2020@vitstudent.ac.in

Department of Mathematics,
School of Advanced Sciences,
VIT Chennai Campus, Chennai - 600 048,
India.
E-mail: keerthivitmaths@gmail.com, sruthakeerthi.b@vit.ac.in

 

Abstract:

In this paper, we introduce a new general subclass of analytic functions with respect to symmetric points in the domain of sine function. We obtain sharp coefficient bounds and upper bounds for the Fekete-Szegö functional. Also we get sharp bounds for the logarithmic coefficients of functions belonging to this new class.

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Paper's Title:

On the Oscillatory Behavior of Self Adjoint Fractional Extensible Beam Equations

Author(s):

S. Priyadharshini¹, G.E. Chatzarakis², S. L. Panetsos² and V. Sadhasivam¹

¹Post Graduate and Research Department of Mathematics,
Thiruvalluvar Government Arts College,
Rasipuram - 637 401, Namakkal Dt., Tamil Nadu,
India.
E-mail: s.priya25april@gmail.com, ovsadha@gmail.com

²Department of Electrical and Electronic Engineering Educators,
School of Pedagogical and Technological Education(ASPETE),
Marousi 15122, Athens,
Greece.
E-mail: geaxatz@otenet.gr, gea.xatz@aspete.gr, spanetsos@aspete.gr

Abstract:

The main objective of this paper is to study the oscillatory behavior of the solutions of self adjoint fractional extensible beam equations by using integral average method. Some new sufficient conditions are established with various boundary conditions over a cylindrical domains. Examples illustrating the results are given.

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Paper's Title:

Some Nonlinear Gronwall-Bellman Type Retarded Integral Inequalities with Power and Their Applications

Author(s):

Ammar Boudeliou

Department of Mathematics, University of Constantine 1 Brothers Mentouri,
BP, 325, Ain El Bey Street, 25017,
Algeria.
E-mail: ammar_boudeliou@umc.edu.dz

Abstract:

In this paper, we investigate a certain class of nonlinear Gronwall-Bellman type integral inequalities with power in more general cases involving retarded term and more general nonlinearities. Our results generalize some known integral inequalities and other results obtained very recently. The inequalities given here can be used to estimate the bound on the solutions of retarded integral equation of Volterra type and integro-differential equations (IDE) with power. Two examples are given to show the validity of our established theorems.

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Paper's Title:

Inequalities Relating to the Gamma Function

Author(s):

Chao-Ping Chen and Feng Qi

Department of Applied Mathematics and Informatics, Research Institute of Applied Mathematics,
Henan Polytechnic University, Jiaozuo City, Henan 454000, China
chenchaoping@hpu.edu.cn

Department of Applied Mathematics and Informatics, Research Institute of Applied Mathematics,
Henan Polytechnic University, Jiaozuo City, Henan 454000, China
qifeng@hpu.edu.cn, fengqi618@member.ams.org
Url: http://rgmia.vu.edu.au/qi.html, http://dami.hpu.edu.cn/qifeng.html

Abstract:

For , we have

                                     .

For,

                                    ,

 

 

And equality occurs for x=1.

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Paper's Title:

Error estimates for aproximations of the Fourier transform of functions in Lp spaces

Author(s):

A. Aglic Aljinovic and J. Pecaric

 

Department of Applied Mathematics,
Faculty of Electrical Engineering and Computing,
University Of Zagreb, Unska 3, 10 000 Zagreb,
Croatia
andrea@zpm.fer.hr

Faculty of Textile Technology,
University of Zagreb, Pierottijeva 6, 10000 Zagreb,
Croatia
pecaric@hazu.hr

 

Abstract:

New inequalities concerning the Fourier transform are given. Estimates of the difference between two Fourier transforms and even bounds to the associated numerical quadrature formulae are provided as well.

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Paper's Title:

Boundary Value Problems for Fractional Diffusion-Wave equation

Author(s):

Varsha Daftardar-Gejji and Hossein Jafari

Department of Mathematics, University of Pune,
Ganeshkhind, Pune - 411007,
INDIA.
vsgejji@math.unipune.ernet.in
jafari_h@math.com

Abstract:

Non homogeneous fractional diffusion-wave equation has been solved under linear/nonlinear boundary conditions. As the order of time derivative changes from 0 to 2, the process changes from slow diffusion to classical diffusion to mixed diffusion-wave behaviour.
Numerical examples presented here confirm this inference. Orthogonality of eigenfunctions in case of fractional Stürm-Liouville problem has been established

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Paper's Title:

Note on the Rank of Birkhoff Interpolation

Author(s):

J. Rubió-Massegú

Applied Mathematics III, Universitat Politècnica de Catalunya,
Colom 1, 08222, Terrassa,
Spain
josep.rubio@upc.edu

Abstract:

The relationship between a variant of the rank of a univariate Birkhoff interpolation problem, called normal rank, and other numbers of interest associated to the interpolation problem is studied.

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Paper's Title:

On Positive Entire Solutions of Second Order Quasilinear Elliptic Equations

Author(s):

Zuodong Yang and Honghui Yin

Institute of Mathematics, School of Mathematics and Computer Science,
Nanjing Normal University, Jiangsu Nanjing 210097,
China;
zdyang_jin@263.net

Department of Mathematics, Huaiyin Teachers College,
Jiangsu Huaian 223001,
China;
School of Mathematics and Computer Sciences,
Nanjing Normal University, Jiangsu Nanjing 210097,
China.
yin_hh@sina.com

Abstract:

In this paper, our main purpose is to establish the existence theorem of positive entire solutions of second order quasilinear elliptic equations under new conditions. The main results of the present paper are new and extend the previously known results.

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Paper's Title:

Iterated Order of Fast Growth Solutions of Linear Differential Equations

Author(s):

Benharrat Belaïdi

Department of Mathematics
Laboratory of Pure and Applied Mathematics
University of Mostaganem
B. P. 227 Mostaganem,
ALGERIA.
belaidi@univ-mosta.dz

Abstract:

In this paper, we investigate the growth of solutions of the differential equation f^(k) + A_k-1 (z) f^(k-1) +...+ A₁ (z) f' + A₀ (z) f= F (z), where A_o (z), ..., A_k-1 (z) and F (z) 0 are entire functions. Some estimates are given for the iterated order of solutions of the above quation when one of the coefficients A_s is being dominant in the sense that it has larger growth than A_j (j≠s) and F.

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Paper's Title:

On Oscillation of Second-Order Delay Dynamic Equations on Time Scales

Author(s):

S. H. Saker

Department of Mathematics, Faculty of Science,
Mansoura University, Mansoura, 35516,
Egypt.
shsaker@mans.edu.eg

Abstract:

Some new oscillation criteria for second-order linear delay dynamic equation on a time scale T are established. Our results improve the recent results for delay dynamic equations and in the special case when T=R, the results include the oscillation results established by Hille [1948, Trans. Amer. Math. Soc. 64 (1948), 234-252] and Erbe [Canad. Math. Bull. 16 (1973), 49-56.] for differential equations. When T=Z the results include and improve some oscillation criteria for difference equations. When T=hZ, h>0, T=q^N and T=N², i.e., for generalized second order delay difference equations our results are essentially new and can be applied on different types of time scales. An example is considered to illustrate the main results.

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Paper's Title:

Some Inequalities for a Certain Class of Multivalent Functions Using Multiplier Transformation

Author(s):

K. Suchithra, B. Adolf Stephen, A. Gangadharan and S. Sivasubramanian

Department Of Applied Mathematics
Sri Venkateswara College Of Engineering
Sriperumbudur, Chennai - 602105,
India.
suchithravenkat@yahoo.co.in

Department Of Mathematics,
Madras Christian College
Chennai - 600059,
India.
adolfmcc2003@yahoo.co.in

Department Of Applied Mathematics
Sri Venkateswara College Of Engineering
Sriperumbudur, Chennai - 602105,
India.
ganga@svce.ac.in

Department Of Mathematics,
Easwari Engineering College
Ramapuram, Chennai - 600089,
India.
ganga@svce.ac.in

Abstract:

The object of the present paper is to derive several inequalities associated with differential subordinations between analytic functions and a linear operator defined for a certain family of p-valent functions, which is introduced here by means of a family of extended multiplier transformations. Some special cases and consequences of the main results are also considered.

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Paper's Title:

Error Inequalities for Weighted Integration Formulae and Applications

Author(s):

Nenad Ujević and Ivan Lekić

Department of Mathematics
University of Split
Teslina 12/III, 21000 Split
CROATIA.
ujevic@pmfst.hr
ivalek@pmfst.hr

Abstract:

Weighted integration formulae are derived. Error inequalities for the weighted integration formulae are obtained. Applications to some special functions are also given.

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Paper's Title:

Fekete-Szegö Problem for Univalent Functions with Respect to k-Symmetric Points

Author(s):

K. Al-Shaqsi and M. Darus

School of Mathematical Sciences, Faculty of Science and Technology,
University Kebangsaan Malaysia,
Bangi 43600 Selangor D. Ehsan,
Malaysia
ommath@hotmail.com
maslina@ukm.my 

Abstract:

In the present investigation, sharp upper bounds of |a₃- μa₂²| for functions f(z) = z + a₂z² + a₂z³ + ... belonging to certain subclasses of starlike and convex functions with respect to k-symmetric points are obtained. Also certain applications of the main results for subclasses of functions defined by convolution with a normalized analytic function are given. In particular, Fekete- Szegö inequalities for certain classes of functions defined through fractional derivatives are obtained.

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Paper's Title:

Linearly Transformable Minimal Surfaces

Author(s):

Harold R. Parks and Walter B. Woods

Department of Mathematics, Oregon State University,
Corvallis, Oregon 97331--4605,
USA
parks@math.oregonstate.edu
URL: http://www.math.oregonstate.edu/people/view/parks/

Abstract:

We give a complete description of a nonplanar minimal surface in R³ with the surprising property that the surface remains minimal after mapping by a linear transformation that dilates by three distinct factors in three orthogonal directions. The surface is defined in closed form using Jacobi elliptic functions.

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Paper's Title:

Ellipses of Minimal Area and of Minimal Eccentricity Circumscribed About a Convex Quadrilateral

Author(s):

Alan Horwitz

Penn State University,
25 Yearsley Mill Rd.,
Media, PA 19063,
U.S.A
alh4@psu.edu

Abstract:

First, we fill in key gaps in Steiner's nice characterization of the most nearly circular ellipse which passes through the vertices of a convex quadrilateral, . Steiner proved that there is only one pair of conjugate directions, M₁ and M₂, that belong to all ellipses of circumscription. Then he proves that if there is an ellipse, E, whose equal conjugate diameters possess the directional constants M₁ and M₂, then E must be an ellipse of circumscription which has minimal eccentricity. However, Steiner does not show the existence or uniqueness of such an ellipse. We prove that there is a unique ellipse of minimal eccentricity which passes through the vertices of  . We also show that there exists an ellipse which passes through the vertices of and whose equal conjugate diameters possess the directional constants M₁ and M₂. We also show that there exists a unique ellipse of minimal area which passes through the vertices of . Finally, we call a convex quadrilateral, , bielliptic if the unique inscribed and circumscribed ellipses of minimal eccentricity have the same eccentricity. This generalizes the notion of bicentric quadrilaterals. In particular, we show the existence of a bielliptic convex quadrilateral which is not bicentric.

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Paper's Title:

The Square Number by the Approximation

Author(s):

Masaki Hisasue

Asahikawa Fuji Girls' High School
Asahikawa Hanasaki-cho 6-3899
Hokkaido, Japan

masaki@fuji.ed.jp
 

Abstract:

In this paper, we give square numbers by using the solutions of Pell's equation.
 

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Paper's Title:

Turan Type Inequalities for Some Special Functions

Author(s):

W. T. Sulaiman

Department of Computer Engineering,
College of Engineering,
University of Mosul,
Iraq

waadsulaiman@hotmail.com

 

Abstract:

In this paper new results concerning the q-polygamma and q-zeta functions are presented. Other generealizations of some known results are also obtained.

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Paper's Title:

Subordination Results Associated with Hadamard Product

Author(s):

S. Sivasubramanian, C. Ramachandran and B. A. Frasin

Department of Mathematics,
University College of Engineering,
Anna University,
Saram-604 307,
India

sivasaisastha@rediffmail.com

Department of Mathematics,
University College of Engineering,
Anna University,
Villupuram,
India

crjsp2004@yahoo.com

Department of Mathematics,
Al al-Bayt University,
P.O. Box: 130095 Mafraq,
Jordan

bafrasin@yahoo.com


 

Abstract:

In the present investigation, we consider an unified class of functions of complex order using Hadamard's convolution. We obtain a necessary and sufficient condition for functions to be in these classes.

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Paper's Title:

On Opial's Inequality for Functions of n-Independent Variables

Author(s):

S. A. A. El-Marouf and S. A. AL-Oufi

Department of Mathematics,
Faculty of Science,
Minoufiya University,
Shebin El-Koom,
Egypt

Department of Mathematics,
Faculty of Science, Taibah University,
Madenahmonwarah,
Kingdom of Saudia Arabia
 

Abstract:

In this paper, we introduce Opial inequalities for functions of n-independent variables. Also, we discuss some different forms of Opial inequality containing functions of n independent variables and their partial derivatives with respect to independent variables.

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Paper's Title:

A Differential Sandwich Theorem for Analytic Functions Defined by the Generalized Sălăgean Operator

Author(s):

D. Răducanu and V. O. Nechita

Faculty of Mathematics and Computer Science,
"Transilvania" University Braşov
Str. Iuliu Maniu 50, 500091 Braşov,
Romania
dorinaraducanu@yahoo.com

Faculty of Mathematics and Computer Science,
"Babeş-Bolyai" University Cluj-Napoca,
Str. M. Kogalniceanu 1, 400084 Cluj-Napoca,
Romania
URL: http://math.ubbcluj.ro/~vnechita/
vnechita@math.ubbcluj.ro
 

Abstract:

We obtain some subordination and superordination results involving the generalized Sălăgean differential operator for certain normalized analytic functions in the open unit disk. Our results extend corresponding previously known results.

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Paper's Title:

Fejér-type Inequalities

Author(s):

Nicuşor Minculete and Flavia-Corina Mitroi

"Dimitrie Cantemir" University,
107 Bisericii Române Street, Braşov, 500068,
România
minculeten@yahoo.com 

University of Craiova, Department of Mathematics,
Street A. I. Cuza 13, Craiova, RO-200585,
Romania
fcmitroi@yahoo.com 
 

Abstract:

The aim of this paper is to present some new Fejér-type results for convex functions. Improvements of Young's inequality (the arithmetic-geometric mean inequality) and other applications to special means are pointed as well.

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Paper's Title:

A Note on Mixed Norm Spaces of Analytic Functions

Author(s):

K. Avetisyan  

Faculty of Physics, Yerevan State University,
Alex Manoogian st. 1, Yerevan, 375025,
Armenia
avetkaren@ysu.am

Abstract:

A direct and elementary proof of an estimate of Littlewood is given together with an application concerning the sharpness and strictness of some inclusions in mixed norm spaces of analytic functions.

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Paper's Title:

Some Distortion and Other Properties Associated with a Family of the n-Fold Symmetric Koebe Type Functions

Author(s):

H. M. Srivastava, N. Tuneski and E. Georgieva-Celakoska

Department of Mathematics and Statistics, University of Victoria,
Victoria, British Columbia V8W 3R4,
Canada

harimsri@math.uvic.ca

Faculty of Mechanical Engineering, St.
Cyril and Methodius University,
Karpo'v s II b.b., MK-1000 Skopje,
Republic of Macedonia

nikolat@mf.edu.mk

cemil@mf.edu.mk
 

Abstract:

In a recent work by Kamali and Srivastava [5], a certain family of the n-fold symmetric Koebe type functions was introduced and studied systematically. In an earlier investigation, Eguchi and Owa [4] had considered its special case when n=1 (see also [10]). Here, in our present sequel to these earlier works, this general family of the n-fold symmetric Koebe type functions is studied further and several distortion theorems and such other properties as the radii of spirallikeness, the radii of starlikeness and the radii of convexity, which are associated with this family of the n-fold symmetric Koebe type functions, are obtained. We also provide certain criteria that embed this family of the n-fold symmetric Koebe type functions in a function class G_λ which was introduced and studied earlier by Silverman [7].

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Paper's Title:

Some New Nonlinear Integro-Differential Inequalities of Gronwall-Bellman-Pachpatte Type

Author(s):

A. ABDELDAIM

Department of Mathematics and Computer Sciences,
Faculty of Science,
Port Said University, Port Said,
EGYPT.

Department of Mathematics,
Faculty of Science and Humanities,
Shaqra University, Dawadmi,
SAUDI ARABIA.

E-mail: ahassen@su.edu.sa
URL: http://faculty.ksu.edu.sa/DRABDELDAIM/Pages/Home.aspx

Abstract:

In this paper we establish some new nonlinear integro-differential inequalities of Gronwall-Bellman-Pachpatte type for function of one independent variable. The purpose of this paper is to extend certain results which proved by Pachpatte in [On some fundamental integrodifferential and integral inequalities, An. Sti. Univ. Al. I. Cuza, Iasi, Vol.23 (1977), 77-86]. The inequalities obtained here can be used in the theory of some new classes of nonlinear integro-differential equations. Some applications are also given to illustrate the usefulness of our results.

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Paper's Title:

Scope of the Logarithmic Mean

Author(s):

Murali Rao and Agnish Dey

Department of Mathematics,
University of Florida,
1400 Stadium Road, Gainesville,
Florida 32611,
U. S. A.

E-mail: mrao@ufl.edu

URL: http://people.clas.ufl.edu/mrao

E-mail: agnish@ufl.edu

URL: http://people.clas.ufl.edu/agnish 

Abstract:

A number a is between two numbers x and y if and only if a is a convex combination of x and y, in other words, it is a "weighted mean" of x and y. Geometric mean, arithmetic mean are well known examples of these "means". Of more recent vintage is the logarithmic mean which has been considered in many articles in the literature. In this note, we first discuss some of its properties. Then we shall introduce the L function and explore the inverse of this function and its connection with the Lambert's Omega function.

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Paper's Title:

Sufficient Conditions for Certain Types of Functions to be Parabolic Starlike

Author(s):

A. Gangadharan and S. Chinthamani

Department of Mathematics,
Easwari Engineering College,
Ramapuram, Chennai - 89,
India.

Research Scholar,
Anna University,
Chennai

E-mail: ganga.megalai@gmail.com

E-mail: chinvicky@rediffmail.com

Abstract:

In this paper sufficient conditions are determined for functions of the form and certain other types of functions to be parabolic starlike.

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Paper's Title:

Properties of q-gamma and q-beta functions derived from the q-Gauss-Pólya inequalities

Author(s):

Sanja Varošanec

Department of Mathematics,
University of Zagreb,
Zagreb, Croatia
E-mail: varosans@math.hr

Abstract:

We consider log-convexity and other properties of several functions related to q-gamma and q-beta functions. These properties are consequences of the general inequality, so-called q-analogue of the Gauss-Pólya inequality. Various inequalities involving these special functions are also given.

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Paper's Title:

Some properties of k-quasi class Q* operators

Author(s):

Shqipe Lohaj and Valdete Rexhëbeqaj Hamiti

Department of Mathematics,
Faculty of Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000,
Kosova.
E-mail: shqipe.lohaj@uni-pr.edu

Department of Mathematics,
Faculty of Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000,
Kosova.
E-mail: valdete.rexhebeqaj@uni-pr.edu

Abstract:

In this paper, we give some results of k-quasi class Q^* operators. We proved that if T is an invertible operator and N be an operator such that N commutes with T^*T, then N is k-quasi class Q^* if and only if TNT^-1 is of k-quasi class Q^*. With example we proved that exist an operator k-quasi class Q^* which is quasi nilpotent but it is not quasi hyponormal.

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Paper's Title:

Coefficient Estimates for Certain Subclasses of Bi-univalent Sakaguchi Type Functions by using Faber Polynomial

Author(s):

P. Murugabharathi, B. Srutha Keerthi

Mathematics Division,
School of Advanced Sciences,
VIT Chennai, Vandaloor, Kelambakkam Road,
Chennai - 600 127, India.
E-mail: bharathi.muhi@gmail.com
E-mail: sruthilaya06@yahoo.co.in

Abstract:

In this work, considering a general subclass of bi-univalent Sakaguchi type functions, we determine estimates for the general Taylor-Maclaurin coefficients of the functions in these classes. For this purpose, we use the Faber polynomial expansions. In certain cases, our estimates improve some of those existing coefficient bounds.

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Paper's Title:

A kind of Function Series and Its Applications

Author(s):

Yang Tianze

Mechanical Engineering,
Shandong University, Xinglongshan Campus,
Jinan, Shandong,
China.

E-mail: qdyangtianze@163.com

Abstract:

A kind of new function series is obtained in this paper. Their theorems and proofs are shown, and some applications are given. We give the expansion form of general integral and the series expansion form of function and the general expansion form of derivative. Using them in the mathematics,we get some unexpected result.

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Paper's Title:

On Euler's First Transformation Formula for k-hypergeometric Function

Author(s):

Sungtae Jun and Insuk Kim

General Education Institute,
Konkuk University, Chungju 380-701,
Republic of Korea.
E-mail: sjun@kku.ac.kr

Department of Mathematics Education,
Wonkwang University, Iksan, 570-749,
Republic of Korea.
E-mail: iki@wku.ac.kr

Abstract:

Mubeen et al. obtained Kummer's first transformation for the k-hypergeometric function. The aim of this note is to provide the Euler-type first transformation for the k-hypergeometric function. As a limiting case, we recover the results of Mubeen et al. In addition to this, an alternate and easy derivation of Kummer's first transformation for the k-hypergeometric function is also given.

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Paper's Title:

The RAFU remainder in Taylor's formula

Author(s):

A. C. Sanchez

''Santa Eulalia'' High School,
Spain
E-mail: csanchezalicia@gmail.com

Abstract:

This work is about the remainder in Taylor's formula. Specifically, the RAFU remainder is studied. Its mathematical expression is given. Some examples are shown. Different ways to obtain this remainder are developed.

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Paper's Title:

A Regularity of the Weak Solution Gradient of the Dirichlet Problem for Divergent Form Elliptic Equations in Morrey Spaces

Author(s):

Nicky K. Tumalun and Philotheus E. A. Tuerah

Mathematics Department, Universitas Negeri Manado,
Tondano Selatan, Minahasa Regency,
Sulawesi Utara Province,
Indonesia.
E-mail:  nickytumalun@unima.ac.id, pheatuerah@unima.ac.id

Abstract:

In this paper we prove that the gradient of the weak solution of the Dirichlet problem for divergent form elliptic equations, with the known term belongs to the Morrey spaces, is the element of the weak Morrey spaces.

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Paper's Title:

Several New Closed-form Evaluations of the Generalized Hypergeometric Function with Argument 1/16

Author(s):

B. R. Srivatsa Kumar, Insuk Kim and Arjun K. Rathie

Department of Mathematics,
Manipal Institute of Technology,
Manipal Academy of Higher Education,
Manipal 576 104,
India.
E-mail: sri_vatsabr@yahoo.com

Department of Mathematics Education,
Wonkwang University,
Iksan, 54538,
Republic of Korea.
E-mail: iki@wku.ac.kr

Department of Mathematics,
Vedant College of Engineering and Technology,
Rajasthan Technical University,
Bundi, 323021, Rajasthan,
India.
E-mail: arjunkumarrathie@gmail.com 

Abstract:

The main objective of this paper is to establish as many as thirty new closed-form evaluations of the generalized hypergeometric function _q+1F_q(z) for q= 2, 3, 4. This is achieved by means of separating the generalized hypergeometric function _q+1F_q(z) for q=1, 2, 3, 4, 5 into even and odd components together with the use of several known infinite series involving central binomial coefficients obtained earlier by Ji and Hei \& Ji and Zhang.

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Paper's Title:

Geometrical Properties of Subclass of Analytic Function with Odd Degree

Author(s):

K. Sivagami Sundari and B. Srutha Keerthi

Divison of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology, Chennai Campus, Chennai - 600 127,
India.
E-mail: sivagamisundari.2298@gmail.com 

Divison of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology, Chennai Campus, Chennai - 600 127,
India.
E-mail: keerthivitmaths@gmail.com
 

Abstract:

The objective of the paper is to study the geometrical properties of the class B(λ, t). For which we have proved that the radius is optimal ,(i.e) the number cannot be replaced by a larger one. Additionally, the graphs for various values of t and λ are compared in order to study the sharpness of the coefficient bounds.

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Paper's Title:

Some Ostrowski Type Inequalities for Two Cos-Integral Transforms of Absolutely Continuous Functions

Author(s):

S. S. Dragomir and G. Sorrentino

Mathematics, College Sport, Health and Engineering,
Victoria University, PO Box 14428,
Melbourne City, MC 8001,
Australia.

DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa.
E-mail: sever.dragomir@vu.edu.au
URL: http://rgmia.org/dragomir

Mathematics, First Year College,
Victoria University, PO Box 14428,
Melbourne City, MC 8001,
Australia.
 

Abstract:

For a Lebesgue integrable function f:[a,b] ⊂[0,π]→C we consider the cos-integral transforms


and

We provide in this paper some upper bounds for the quantities

and

for
x ∈ [ a,b], in terms of the p-norms of the derivative f ' for absolutely continuous functions f:[a,b] ⊂[0,π]→C. Applications for approximating Steklov cos-average functions and Steklov split cos-average functions are also provided.

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Paper's Title:

Analytical and Numerical Solutions of the Inhomogenous Wave Equation

Author(s):

T. Matsuura and S. Saitoh

Department of Mechanical Engineering, Faculty of Engineering,
Gunma University, Kiryu 376-8515, Japan
matsuura@me.gunma-u.ac.jp

Department of Mathematics, Faculty of Engineering,
Gunma University, Kiryu 376-8515, Japan
ssaitoh@math.sci.gunma-u.ac.jp

 

Abstract:

In this paper, by a new concept and method we give approximate solutions of the inhomogenous wave equation on multidimensional spaces. Numerical experiments are conducted as well.

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Paper's Title:

Monotonicity Properties for Generalized Logarithmic Means

Author(s):

Chao-Ping Chen and Feng Qi

Department of Applied Mathematics and Informatics, Research Institute of Applied Mathematics,
Henan Polytechnic University, Jiaozuo City, Henan 454000, China
chenchaoping@hpu.edu.cn

Department of Applied Mathematics and Informatics, Research Institute of Applied Mathematics,
Henan Polytechnic University, Jiaozuo City, Henan 454000, China
qifeng@hpu.edu.cn, fengqi618@member.ams.org
Url: http://rgmia.vu.edu.au/qi.html, http://dami.hpu.edu.cn/qifeng.html

Abstract:

In this paper, we consider the monotonicity properties for ratio of two generalized logarithmic means, and then use it to extend and complement a recently published result of F. Qi and B.-N. Guo.

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Paper's Title:

A Majorization Problem for the Subclass of p-Valently Analytic Functions of Complex Order

Author(s):

Sezgin Akbulut

Department of Mathematics, Science and Art Faculty,
Atatürk University, 25240 Erzurum, Turkey
sbulut@atauni.edu.tr

Abstract:

The main purpose of this paper is to investigate a majorization problem for the class . Relevant connections of the main result obtained in this paper with those given by earlier workers on the subject are also pointed out.

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Paper's Title:

New Proofs of the Grüss Inequality

Author(s):

A.Mc.D. Mercer and Peter R. Mercer

Dept. Mathematics and Statistics,
University of Guelph, Guelph, Ontario,
Canada.
amercer@reach.net

Dept. Mathematics,
S.U.N.Y. College at Buffalo, Buffalo, NY,
U.S.A.
mercerpr@math.buffalostate.edu
 

 

Abstract:

We present new proofs of the Grüss inequality in its original form and in its linear functional form.

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Paper's Title:

Reverse of Martin's Inequality

Author(s):

Chao-Ping Chen, Feng Qi, and Sever S. Dragomir

Department of Applied Mathematics and Informatics,
Research Institute of Applied Mathematics,
Henan Polytechnic University,
Jiaozuo City, Henan 454010, China
chenchaoping@sohu.com; chenchaoping@hpu.edu.cn 

Department of Applied Mathematics and Informatics,
Research Institute of Applied Mathematics,
Henan Polytechnic University,
Jiaozuo City, Henan 454010, China
qifeng@hpu.edu.cn 
Url: http://rgmia.vu.edu.au/qi.html

School of Computer Science and Mathematics,
Victoria University of Technology,
P. O. Box 14428, Melbourne City Mc,
Victoria 8001, Australia
Sever.Dragomir@vu.edu.au 
Url: http://rgmia.vu.edu.au/SSDragomirWeb.html 

Abstract:

In this paper, it is proved that

for all natural numbers n, and all real r < 0.

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Paper's Title:

Some Generalizations of Steffensen's Inequality

Author(s):

W. T. Sulaiman

College of Computer Science and Mathematics
University of Mosul , Iraq

Abstract:

Some generalization of Steffensen's inequalities are given.

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Paper's Title:

Classes of Meromorphic p-valent Parabolic Starlike Functions with Positive Coefficients

Author(s):

S. Sivaprasad Kumar, V. Ravichandran, and G. Murugusundaramoorthy

Department of Applied Mathematics
Delhi College of Engineering,
Delhi 110042, India
sivpk71@yahoo.com

School of Mathematical Sciences
Universiti Sains Malaysia
11800 USM Penang
Malaysia
vravi@cs.usm.my
URL: http://cs.usm.my/~vravi

Department of Mathematics
Vellore Institute of Technology (Deemed University)
Vellore 632 014, India
gmsmoorthy@yahoo.com

Abstract:

In the present paper, we consider two general subclasses of meromorphic p-valent starlike functions with positive coefficients and obtain a necessary and sufficient condition for functions to be in these classes. Also we obtain certain other related results as a consequences of our main results.

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Paper's Title:

A general common fixed point theorem for reciprocally continuous mappings satisfying an implicit relation

Author(s):

A. Djoudi and A. Aliouche

Faculty of Science, University of Annaba,
P.O. Box 23000, Annaba,
Algeria.
adjoudi@yahoo.com

Department of Mathematics, University of Larbi Ben M'Hidi,
Oum-El-Bouaghi 04000,
Algeria.
abdmath@hotmail.com

Abstract:

A general common fixed point theorem for compatible mappings satisfying an implicit relation is obtained by replacing the continuity of one mapping by the reciprocal continuity of two mappings.

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Paper's Title:

p-valent Meromorphic Functions Involving Hypergeometric and Koebe Functions by Using Differential Operator

Author(s):

S. Najafzadeh, S. R. Kulkarni and G. Murugusundaramoorthy

Department of Mathematics,
Fergusson College, Pune University,
Pune - 411004,
India.
Najafzadeh1234@yahoo.ie
kulkarni_ferg@yahoo.com

School of Science and Humanities,
Vellore Institute of Technology, Deemed University,
Vellore - 632014,
India.
gmsmoorthy@yahoo.com

Abstract:

New classes of multivalent meromorphic functions involving hypergeometric and Koebe functions are introduced,we find some properties of these classes e.g. distortion bounds, radii of starlikeness and convexity, extreme points, Hadamard product and verify effect of some integral operator on members of these classes.

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Paper's Title:

Algebraic Approach to the Fractional Derivatives

Author(s):

Kostadin Trenčevski and Živorad Tomovski

Institute of Mathematics,
St. Cyril and Methodius University,
P.O. Box 162, 1000 Skopje,
Macedonia
kostatre@iunona.pmf.ukim.edu.mk

tomovski@iunona.pmf.ukim.edu.mk

URL:http://www.pmf.ukim.edu.mk

Abstract:

In this paper we introduce an alternative definition of the fractional derivatives and also a characteristic class of so called ideal functions, which admit arbitrary fractional derivatives (also integrals). Further some ideal functions are found, which lead to representations of the Bernoulli and Euler numbers B_k and E_k for any real number k, via fractional derivatives of some functions at x=0.

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Paper's Title:

On the Fekete-Szegő Inequality for Some Subclasses of Analytic Functions

Author(s):

T.N. Shanmugam and A. Singaravelu

Department of Mathematics,
College of Engineering,
Anna University, Chennai-600 025,
Tamilnadu, India
shan@annauniv.edu

Department of Mathematics,
Valliammai Engineering College,
Chennai-603 203,
Tamilnadu, India
sivasaisastha@rediffmail.com

Abstract:

In this present investigation, the authors obtainFekete-Szegő's inequality for certain normalized analytic functions defined on the open unit disk for which lie in a region starlike with respect to 1 and symmetric with respect to the real axis. Also certain applications of the main result for a class of functions defined by convolution are given. As a special case of this result, Fekete-Szegő's inequality for a class of functions defined through fractional derivatives is also obtained.

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Paper's Title:

Generalized Hypergeometric Functions Defined on the Class of Univalent Functions

Author(s):

N. Marikkannan, A. Gangadharan and C. Ganesamoorthy

Department of Applied Mathematics,
Sri Venkateswara College of Engineering,
Sriperumbudur 602105,
India.
mari@svce.ac.in

Department of Applied mathematics,
Sri Venkateswara College of Engineering,
Sriperumbudur 602105,
India.
ganga@svce.ac.in

Department of Mathematics,
Alagappa university,
Karaikudi,
India.
ganesamoorthyc@yahoo.com

Abstract:

Let A denotes the class of all analytic functions f(z), normalized by the condition f'(0)-1=f(0)=0 defined on the open unit disk Δ and S be the subclass of A containing univalent functions of A. In this paper, we find the sufficient conditions for hypergeometric functions defined on S to be in certain subclasses of A, like k-UCV, k-ST

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Paper's Title:

On an Integral Inequality of the Hardy-Type

Author(s):

C. O. Imoru and A. G. Adeagbo-Sheikh

Department of Mathematics
Obafemi Awolowo University, Ile-Ife, Nigeria.
cimoru@oauife.edu.ng
asheikh@oauife.edu.ng

Abstract:

In this paper, we obtain an integral inequality which extends Shum's and Imoru's generalization of Hardy's Inequality. Our main tool is Imoru's adaptation of Jensen's Inequality for convex functions.

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Paper's Title:

On Sandwich Theorems for Certain Subclass of Analytic Functions Involving Dziok-Srivastava Operator

Author(s):

T. N. Shanmugam, M. P. Jeyarama and A. Singaravelu

Department of Mathematics
College of Engineering, Anna University
Chennai - 600 025,
India
drtns2001@yahoo.com

Department of Mathematics
Easwari Engineering College
Ramapuram, Chennai - 600089
Tamilnadu, India
jeyaraman-mp@yahoo.co.i

Department of Mathematics
Valliammai Engineering College
Chennai - 603203
Tamilnadu, India.
asing-59@yahoo.com

Abstract:

The purpose of this present paper is to derive some subordination and superordination results for certain normalized analytic functions in the open unit disk, acted upon by Dziok-Srivastava operator. Relevant connections of the results, which are presented in this paper, with various known results are also considered.

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Paper's Title:

The Bernoulli Inequality in Uniformly Complete f-algebras with Identity

Author(s):

Adel Toumi and Mohamed Ali Toumi

Laboratoire de Physique des Liquides Critiques, Département de Physique, Faculté des Sciences de Bizerte, 7021, Zarzouna, Bizerte, TUNISIA
Adel.Toumi@fst.rnu.tn

Département de Mathématiques, Faculté des Sciences de Bizerte, 7021, Zarzouna, Bizerte, TUNISIA
MohamedAli.Toumi@fsb.rnu.tn

Abstract:

The main purpose of this paper is to establish with a constructive proof the Bernoulli inequality: let A be a uniformly complete f-algebra with e as unit element, let 1<p<∞, then

(e+a)^p≥e+pa

for all a∈A₊. As an application we prove the Hölder inequality for positive linear functionals on a uniformly complete f-algebra with identity by using the Minkowski inequality.

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Paper's Title:

On a Class of Uniformly Convex Functions Defined by Convolution with Fixed Coefficient

Author(s):

T. N. Shanmugam, S. Sivasubramanian, and G. Murugusundaramoorthy

Department of Mathematics,
College of Engineering,
Anna University,
Chennai - 600 025,
India.
 drtns2001@yahoo.com

 Department of Mathematics,
University College of Engineering,
Tindivanam
Anna University-Chennai,
Saram-604 703,
India.
sivasaisastha@rediffmail.com

 School of Sciences and Humanities,
VIT University, Vellore-632 014,
India.
gmsmoorthy@yahoo.com

Abstract:

We define a new subclass of uniformly convex functions with negative and fixed second coefficients defined by convolution. The main object of this paper is to obtain coefficient estimates distortion bounds, closure theorems and extreme points for functions belong to this new class . The results are generalized to families with fixed finitely many coefficients.

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Paper's Title:

Two Remarks on Commutators of Hardy Operator

Author(s):

Yasuo Komori-Furuya

School of High Technology for Human Welfare 
Tokai University
317 Nishino Numazu, Shizuoka 410-0395 Japan
komori@wing.ncc.u-tokai.ac.jp  

Abstract:

Fu and Lu showed that
the commutator of multiplication operator by b and
the n-dimensional Hardy operator
is bounded on L^p if b is in some CMO space.
We shall prove the converse of this theorem
and also prove that their result is optimal by giving a counterexample

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Paper's Title:

An L^p Inequality for `Self-Reciprocal' Polynomials. II

Author(s):

M. A. Qazi

Department of Mathematics,
Tuskegee University,
Tuskegee, Alabama 36088
U.S.A.

qazima@aol.com

 

Abstract:

The main result of this paper is a sharp integral mean inequality for the derivative of a `self-reciprocal' polynomial.

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Paper's Title:

Error Estimates for Approximations of the Laplace transform of Functions in L_p Spaces

Author(s):

Andrea Aglić Aljinović

Department of Applied Mathematics,
Faculty of Electrical Engineering and Computing,
University of Zagreb,
Unska 3, 10 000 Zagreb,
Croatia

andrea.aglic@fer.hr 

 

Abstract:

In this paper error estimates of approximations in complex domain for the Laplace transform are given for functions which vanish beyond a finite domain and whose derivatives belongs to L_p spaces. New inequalities concerning the Laplace transform, as well as estimates of the difference between the two Laplace transforms are presented and used to obtain two associated numerical rules and error bounds of their remainders.

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Paper's Title:

Finite and Infinite Order Solutions of a Class of Higher Order Linear Differential Equations

Author(s):

Saada Hamouda

Department of Mathematics,
Laboratory of Pure and Applied Mathematics,
University of Mostaganem, B. P 227 Mostaganem,
ALGERIA
hamouda_saada@yahoo.fr

Abstract:

In this paper, we investigate the growth of solutions of higher order linear differential equations where most of the coefficients have the same order and type with each other.

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Paper's Title:

Necessary and Sufficient Conditions for Cyclic Homogeneous Polynomial Inequalities of Degree Four in Real Variables

Author(s):

Vasile Cirtoaje and Yuanzhe Zhou

Department of Automatic Control and Computers
University of Ploiesti
Romania.
vcirtoaje@upg-ploiesti.ro.
 

High School Affiliated to Wuhan University, China

 

Abstract:

In this paper, we give two sets of necessary and sufficient conditions that the inequality f₄(x,y,z) ≥ 0 holds for any real numbers x,y,z, where f₄(x,y,z) is a cyclic homogeneous polynomial of degree four. In addition, all equality cases of this inequality are analysed. For the particular case in which f₄(1,1,1)=0, we get the main result in [3]. Several applications are given to show the effectiveness of the proposed methods.

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Paper's Title:

A Note on the Ulam stability of Reciprocal Difference and Adjoint Functional Equations

Author(s):

K. Ravi, J. M. Rassias, M. E. Gordji, and B. V. Senthil Kumar

Department of Mathematics,
Sacred Heart College, Tirupattur - 635601,
India
shckavi@yahoo.co.in
 

Pedagogical Department E. E.,
Section of Mathematics and Informatics,
National and Capodistrian University of Athens,
4, Agamemnonos Str., Aghia Paraskevi,
Athens, Attikis 15342,
GREECE
jrassias@primedu.uoa.gr

Department of Mathematics, Semnan University,
P.O. Box 35195-363, Semnan,
Iran
madjid.eshaghi@gmail.com

Department of Mathematics,
C.Abdul Hakeem College of Engineering and
Technology, Melvisharam - 632 509,
India
bvssree@yahoo.co.in

 

Abstract:

This note is an erratum to previous work published as Volume 8, Issue 1, Paper 13, 2011 of The Australian Journal of Mathematical Analysis and Applications.

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Paper's Title:

Solution of Inequalities with Power-Exponential Functions by Cîrtoaje

Author(s):

Masaki Hisasue

Asahikawa fuji girls' high school,
Asahikawa Hanasaki-cho 6-3899, Hokkaido,
Japan

masaki@fuji.ed.jp
 

Abstract:

In this paper, we prove the open inequality a^2b+b^^2a < 1 for all nonnegative real numbers a and b such that a+b=1.

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Paper's Title:

On Some Relations Among the Solutions of the Linear Volterra Integral Equations

Author(s):

Ismet Ozdemir and Faruk Temizer

Inönü Üniversitesi Eğitim Fakültesi,
44280-Malatya,
Turkey

ismet.ozdemir@inonu.edu.tr

omer.temizer@inonu.edu.tr
 

Abstract:

The sufficient conditions for y₁(x)≤ y₂(x) were given in [1] such that y_m(x)=f_m(x)+∫_a^x K_m(x, t)y_m(t)dt,(m=1,2) and x∈ [a, b]. Some properties such as positivity, boundedness and monotonicity of the solution of the linear Volterra integral equation of the form f(t)=1-∫₀^tK(t-τ)f(τ)dτ=1-K*f, (0≤ t<∞) were obtained, without solving this equation, in [3,4,5,6]. Also, the boundaries for functions f', f'',..., f⁽ⁿ⁾,(n ∈ N) defined on the infinite interval [0, ∞) were found in [7,8].

In this work, for the given equation f(t)=1-K* f and n≥ 2, it is derived that there exist the functions  L₂, L₃,..., L_n which can be obtained by means of K and some inequalities among the functions f, h₂, h₃,..., h_i for i=2, 3,...., n are satisfied on the infinite interval [0, ∞), where h_i is the solution of the equation h_i(t)=1-L_i* h_i and n is a natural number.

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Paper's Title:

Certain Coefficient Estimates for Bi-univalent Sakaguchi Type Functions

Author(s):

B. Srutha Keerthi, S. Chinthamani

Department of Applied Mathematics,
Sri Venkateswara College of Engineering,
Sriperumbudur, Chennai - 602105,
India

sruthilaya06@yahoo.co.in

 chinvicky@rediffmail.com

 

Abstract:

Estimates on the initial coefficients are obtained for normalized analytic functions f in the open unit disk with f and its inverse g = f^-1 satisfying the conditions that zf'(z) / f(z) and zg'(z) / g(z) are both subordinate to a starlike univalent function whose range is symmetric with respect to the real axis. Several related classes of functions are also considered, and connections to earlier known results are made.

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Paper's Title:

Certain Compact Generalizations of Well-Known Polynomial Inequalities

Author(s):

N. A. Rather and Suhail Gulzar

Department of Mathematics,
University of Kashmir, Hazratbal Srinagar-190006,
India.

dr.narather@gmail.com

sgmattoo@gmail.com

Abstract:

In this paper, certain sharp compact generalizations of well-known Bernstien-type inequalities for polynomials, from which a variety of interesting results follow as special cases, are obtained.

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Paper's Title:

Existence and Regularity of Minima of an Integral Functional in Unbounded Domain

Author(s):

L. Aharouch, J. Bennouna and A. Bouajaja

King Khalid University
Faculty of Arts and Science Mha'l Asir
Saudi Arabia.

E-mail: laharouch@gmail.com

Université Sidi Mohammed Ben Abdellah
Faculté des Sciences Dhar-Mahraz
B.P 1796 Atlas Fès,
Maroc.

Email: jbennouna@hotmail.com

E-mail: kadabouajaja@hotmail.com

Abstract:

We prove the existence and the regularity of minima for a functional defined on a suitable Sobolev space.

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Paper's Title:

Commutators of Hardy Type Operators

Author(s):

Chunping Xie

Department of Mathematics,
Milwaukee School of Engineering,
1025 N. Broadway,
Milwaukee, Wisconsin 53202,
USA.

E-mail: xie@msoe.edu
URL: http://www.msoe.edu/people/chunping.xie

Abstract:

The note deals with commutaors of the Hardy operator, Hardy type operators on Morrey spaces on R+. We have proved that the commutators generated by Hardy operator and Hardy type operators with a BMO function b are bounded on the Morrey spaces.

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Paper's Title:

Ostrowski Type Fractional Integral Inequalities for Generalized (s,m,φ)-preinvex Functions

Author(s):

Artion Kashuri and Rozana Liko

University of Vlora "Ismail Qemali",
Faculty of Technical Science,
Department of Mathematics, 9400,
Albania.
E-mail: artionkashuri@gmail.com
E-mail: rozanaliko86@gmail.com

Abstract:

In the present paper, the notion of generalized (s,m,φ)-preinvex function is introduced and some new integral inequalities for the left hand side of Gauss-Jacobi type quadrature formula involving generalized (s,m,φ)-preinvex functions along with beta function are given. Moreover, some generalizations of Ostrowski type inequalities for generalized (s,m,φ)-preinvex functions via Riemann-Liouville fractional integrals are established.

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Paper's Title:

On The Rayleigh-Love Rod Accreting In Both Length And Cross-Sectional Area: Forced And Damped Vibrations

Author(s):

M.L.G. Lekalakala¹, M. Shatalov², I. Fedotov³, S.V. Joubert⁴

¹Department of Mathematics, Vaal University of Technology, P.O. Box 1889, Secunda, 2302, South Africa.
E-mail¹: glen@vut.ac.za 

^2,3,4Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria, South Africa.

Abstract:

In this paper an elastic cylindrical rod that is subjected to forced and damped vibrations is considered. The rod is assumed to be isotropic. The applied external force of excitation is assumed to be harmonic, and the damping force is that of Kelvin-Voigt. The longitudinally vibrating rod is fixed at the left end and free at the other end. The rod is assumed to be accreting in length and cross-sectional area as it vibrates. The problem arising and the dynamics of the vibrating rod are described and investigated within the Rayleigh-Love theories of the rod. A partial differential equation describing the longitudinal displacement of the rod is formulated. The formulated partial differential equation, together with the corresponding boundary conditions as per the configuration of the rod, is solved numerically using the Galerkin-Kantorovich method. The frequency of vibration of the harmonic exciting force is kept constant in this investigation.

It is shown that in this periodically forced viscoelastic damped vibration, all the modes of vibration are subjected to the resonance behaviour within a proper time interval, depending on the length of the accreting rod.

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Paper's Title:

A Generalization of Viete's Infinite Product and New Mean Iterations

Author(s):

Ryo Nishimura

Department of Frontier Materials
Nagoya Institute of Technology
Gokiso-cho, Showa-ku, Nagoya
Aichi, 466-8555, Japan.
E-mail: rrnishimura@gmail.com

Abstract:

In this paper, we generalize Viéte's infinite product formula by use of Chebyshev polynomials. Furthermore, the infinite product formula for the lemniscate sine is also generalized. Finally, we obtain new mean iterations by use of these infinite product formulas.

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Paper's Title:

Generalized Weighted Trapezoid and Grüss Type Inequalities on Time Scales

Author(s):

Eze Raymond Nwaeze

Department of Mathematics,
Tuskegee University,
Tuskegee, AL 36088,
USA.
E-mail: enwaeze@mytu.tuskegee.edu

Abstract:

In this work, we obtain some new generalized weighted trapezoid and Grüss type inequalities on time scales for parameter functions. Our results give a broader generalization of the results due to Pachpatte in [14]. In addition, the continuous and discrete cases are also considered from which, other results are obtained.

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Paper's Title:

New Refinements of Hölder's Inequality

Author(s):

Xiu-Fen Ma

College of Mathematical and Computer,
Chongqing Normal University Foreign Trade and Business College,
No.9 of Xuefu Road, Hechuan District 401520,
Chongqing City,
The People's Republic of China.
E-mail: maxiufen86@163.com

Abstract:

In this paper, we define two mappings, investigate their properties, obtain some new refinements of Hölder's inequality.

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Paper's Title:

Extreme Curvature of Polynomials and Level Sets

Author(s):

Stephanie P. Edwards, arah J. Jensen, Edward Niedermeyer, and Lindsay Willett

Department of Mathematics,
Hope College,
Holland, MI 49423,
U.S.A.
E-mail: sedwards@hope.edu
E-mail: tarahjaye@gmail.com
E-mail: eddie.niedermeyer@gmail.com
E-mail: willettlm1@gmail.com
WWW: http://math.hope.edu/sedwards/

Abstract:

Let f be a real polynomial of degree n. Determining the maximum number of zeros of kappa, the curvature of f, is an easy problem: since the zeros of kappa are the zeros of f'', the curvature of f is 0 at most n-2 times. A much more intriguing problem is to determine the maximum number of relative extreme values for the function kappa. Since kappa'=0 at each extreme point of kappa, we are interested in the maximum number of zeros of kappa'. In 2004, the first author and R. Gordon showed that if all the zeros of f'' are real, then f has at most n-1 points of extreme curvature. We use level curves and auxiliary functions to study the zeros of the derivatives of these functions. We provide a partial solution to this problem, showing that f has at most n-1 points of extreme curvature, given certain geometrical conditions. The conjecture that f has at most n-1 points of extreme curvature remains open.

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Paper's Title:

A Note on Calderon Operator

Author(s):

Chunping Xie

Department of Mathematics,
Milwaukee School of Engineering,
1025 N. Broadway,
Milwaukee, Wisconsin 53202,
U. S. A.

E-mail: xie@msoe.edu

URL: http://www.msoe.edu/people/chunping.xie

Abstract:

We have shown that the Calderon operator is bounded on Morrey Spaces on R⁺. Also under certain conditions on the weight, the Hardy operator, the adjoint Hardy operator, and therefore the Caldern operator are bounded on the weighted Morrey spaces.

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Paper's Title:

Integrating Factors and First Integrals of a Class of Third Order Differential Equations

Author(s):

Mohammadkheer Al-Jararha

Department of Mathematics,
Yarmouk University,
Irbid 21163,
Jordan.

E-mail: mohammad.ja@yu.edu.jo

Abstract:

The principle of finding an integrating factor for a none exact differential equations is extended to a class of third order differential equations. If the third order equation is not exact, under certain conditions, an integrating factor exists which transforms it to an exact one. Hence, it can be reduced into a second order differential equation. In this paper, we give explicit forms for certain integrating factors of a class of the third order differential equations.

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Paper's Title:

Corrigendum for New Exact Taylor's Expansions Without the Remainder: Application to Finance

Author(s):

Moawia Alghalith

Economics Dept.,
University of the West Indies,
St Augustine,
Trinidad and Tobago.

E-mail: malghalith@gmail.com

Abstract:

This article is a corrigendum to AJMAA Volume 15, Issue 1, Article 5, PDF Link.

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Paper's Title:

On Finding Integrating Factors and First Integrals for a Class of Higher Order Differential Equations

Author(s):

Mohammadkheer M. Al-Jararha

Department of Mathematics,
Yarmouk University,
Irbid, 21163,
Jordan.
E-mail: mohammad.ja@yu.edu.jo

Abstract:

If the $n-th$ order differential equation is not exact, under certain conditions, an integrating factor exists which transforms the differential equation into an exact one. Thus, the order of differential equation can be reduced to the lower order. In this paper, we present a technique for finding integrating factors of the following class of differential equations:
 

Here, the functions F₀,F₁,F₂, …,F_n are assumed to be continuous functions with their first partial derivatives on some simply connected domain Ω ⊂ Rⁿ⁺¹. We also presented some demonstrative examples

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Paper's Title:

A Note on Taylor Expansions Without the Differentiability Assumption

Author(s):

Moawia Alghalith

Economics Dept.,
University of the West Indies,
St Augustine,
Trinidad and Tobago.

E-mail: malghalith@gmail.com

Abstract:

We introduce new Taylor expansions when the function is not differentiable.

Retraction

This article has been retracted under the authority of the Editor on Chief on 1 April, 2021. The PDF file is no longer available, but can be obtained from the editorial office upon request.

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Paper's Title:

Cubic Alternating Harmonic Number Sums

Author(s):

Anthony Sofo

Victoria University,
College of Engineering and Science,
Melbourne City,
Australia.
E-mail: Anthony.Sofo@vu.edu.au

Abstract:

We develop new closed form representations of sums of cubic alternating harmonic numbers and reciprocal binomial coefficients. We also identify a new integral representation for the ζ (4)  constant.

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Paper's Title:

On Trigonometric Approximation of Continuous Functions by Deferred Matrix Means

Author(s):

Xhevat Zahir Krasniqi

Faculty of Education,
University of Prishtina "Hasan Prishtina",
Avenue "Mother Theresa " no. 5, Prishtinë 10000,
Republic of Kosovo.
E-mail: xhevat.krasniqi@uni-pr.edu
URL: https://staff.uni-pr.edu/profile/xhevatkrasniqi

Abstract:

In this paper, for the first time, we introduce the deferred matrix means which contain the well-known generalized deferred Nörlund, deferred Nörlund, deferred Riesz, deferred Cesàro means introduced earlier by others, and a new class of sequences (predominantly a wider class than the class of Head Bounded Variation Sequences). In addition, using the deferred matrix means of Fourier series of a continuous function, we determine the degree of approximation of such function via its modulus of continuity and a positive mediate function.

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Paper's Title:

Reverse Hölder and Minkowski type integral inequalities for n functions

Author(s):

Panagiotis T. Krasopoulos and Lazhar Bougoffa

Department of Informatics, KEAO,
Electronic National Social Security Fund,
12 Patision St., 10677, Athens,
Greece.
E-mail: pan_kras@yahoo.gr
pankras@teemail.gr

Department of Mathematics,
Faculty of Science, Imam Mohammad Ibn Saud Islamic University,
P.O. Box 90950, Riyadh 11623,
Saudi Arabia.
E-mail: lbbougoffa@imamu.edu.sa
bougoffa@hotmail.com

Abstract:

We present and prove new reverse Hölder and Minkowski type integral inequalities for n functions. We compare our results with other known results from the relative literature in order to test their performance. In this respect, our theorems can be viewed as generalizations of some already known integral inequalities.

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Paper's Title:

Application of Chebyshev Polynomials to Volterra-Fredholm Integral Equations

Author(s):

Aissa Lakhal, Mostefa Nadir and Mohamed Nasseh Nadir

Department of Mathematics,
Faculty of Mathematics and
Informatics,
University of Msila,
Algeria.

E-mail: aissa.lakhal@univ-msila.dz
mostefa.nadir@univ-msila.dz
nadir.mohamednasseh@yahoo.com

URL: https://www.mostefanadir.com

Abstract:

The goal of this work is to examine the numerical solution of linear Volterra-Fredholm integral equations of the second kind using the first, second, third and fourth Chebyshev polynomials. Noting that, the approximate solution is given in the form of series which converges to the exact one. Numerical examples are compared with other methods, in order to prove the applicability and the efficiency of this technical.

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Paper's Title:

Estimation for Bounded Solutions of Some Nonlinear Integral Inequalities with Delay in Several Variables

Author(s):

Smakdji Mohamed Elhadi, Denche Mouhamed and Khellaf Hassane

Department of Mathematics
University of Frères Mentouri
PO Box 25000, Ain Elbay,
Constantine,
Algeria.
E-mail: khellafhassane@umc.edu.dz

Abstract:

In this paper, some new nonlinear retarded integral inequalities of Gronwall-Bellman type for functions of two and n-independents variables are investigated. The derived results can be applied in the study of differential-integral equations with time delay. An example is given to illustrate the application of our results.

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Paper's Title:

On the Class of Totally Polynomially Posinormal Operators

Author(s):

E. Shine Lal, T. Prasad, P. Ramya

Department of Mathematics,University College,
Thiruvananthapuram, Kerala, 695034.
India.
E-mail: shinelal.e@gmail.com

 
Department of Mathematics,
University of Calicut,
Malapuram, Kerala 673635,
India.
E-mail: prasadvalapil@gmail.com

Department of Mathematics,
N.S.S College,
Nemmara, Kerala, 678508
India.
E-mail: ramyagcc@gmail.com

Abstract:

In this paper, we proved that if  T ∈ B(H)  is totally P-posinormal operator with . Moreover, we study spectral continuity and range kernel orthogonality of these class of operators.

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Paper's Title:

Oscillation Criteria for Second Order Delay Difference Equations via Canonical Transformations and Some New Monotonic Properties

Author(s):

R. Deepalakhmi, S. Saravanan, J. R. Graef, and E. Thandapani

Department of Interdisciplinary Studies
Tamil Nadu Dr. Ambedkar Law University
Chennai-600113,
India.
profdeepalakshmi@gmail.com

Madras School of Economics,
Chennai-600025,
India.
profsaran11@gmail.com

Department of Mathematics,
University of Tennessee at Chattanooga,
Chattanooga,TN 37403,
USA.
john-graef@utc.edu

Ramanujan Institute for Advanced Study in Mathematics,
University of Madras,
Chennai - 600 005,
India.
ethandapani@yahoo.co.in

Abstract:

This paper is concerned with second-order linear noncanonical delay difference equations of the form

Δ(μ(t)Δ y(t))+ p(t)y(φ(t))=0.

The authors prove new oscillation criteria by first transforming the equation into canonical form and then obtaining some new monotonic properties of the positive solutions of the transformed equation. By using a comparison with first-order delay difference equations and a generalization of a technique developed by Koplatadze, they obtain their main results. Examples illustrating the improvement over known results in the literature are presented.

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Paper's Title:

Integrability of Sine and Cosine Series Having Coefficients of a New Class

Author(s):

L. Leindler

Bolyai Institute, University of Szeged, Aradi Vértanúk Tere 1, H-6720 Szeged, Hungary
leindler@math.u-szeged.hu

Abstract:

Some integrability theorems or only their sufficient part are generalized such that the coefficients of the sine and cosine series belong to a new class of sequences being wider than the class of sequences of rest bounded variation, which itself is a generalization of the monotone decreasing sequences, but a subclass of the almost monotone decreasing sequences. It is also verified that the new class of sequences and the class of almost monotone decreasing sequences are not comparable.

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Paper's Title:

An Application of Quasi Power Increasing Sequences

Author(s):

Hüseyín Bor

Department of Mathematics, Erciyes University, 38039 Kayseri, Turkey
bor@erciyes.edu.tr
Url: Http://math.erciyes.edu.tr/Hbor.htm

 

Abstract:

In this paper a result of Bor [2] has been proved under weaker conditions by using a -quasi power increasing sequence instead of an almost increasing sequence.

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Paper's Title:

On an Extension of Hilbert’s Integral Inequality with Some Parameters

Author(s):

Bicheng Yang

Department of Mathematics, Guangdong Education College, Guangzhou, Guangdong 510303, People’s Republic of China.
bcyang@pub.guangzhou.gd.cn
URL: http://www1.gdei.edu.cn/yangbicheng/index.html

Abstract:

In this paper, by introducing some parameters and estimating the weight function, we give an extension of Hilbert’s integral inequality with a best constant factor. As applications, we consider the equivalent form and some particular results.

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Paper's Title:

An alternative proof of monotonicity for the extended mean values

Author(s):

Chao-Ping Chen and Feng Qi

Department of Applied Mathematics and Informatics, Research Institute of Applied Mathematics,
Henan Polytechnic University, Jiaozuo City, Henan 454000, China
chenchaoping@hpu.edu.cn

Department of Applied Mathematics and Informatics, Research Institute of Applied Mathematics,
Henan Polytechnic University, Jiaozuo City, Henan 454000, China
qifeng@hpu.edu.cn, fengqi618@member.ams.org
Url: http://rgmia.vu.edu.au/qi.html, http://dami.hpu.edu.cn/qifeng.html

 

Abstract:

An alternative proof of monotonicity for the extended mean values is given.

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Paper's Title:

On the Hohov Convolution Of The Class S_p(α,β)

Author(s):

T. N. Shanmugam and S. Sivasubramanian

Department of Mathematics,
Anna University,
Chennai 600025,
Tamilnadu, India.
shan@annauniv.edu

Department of Mathematics,
Easwari Engineering College,
Chennai-600089,
Tamilnadu, India,
sivasaisastha@rediffmail.com

Abstract:

Let F(a,b;c;z) be the Gaussian hypergeometric function and I_a,b;c(f)=zF(a,b;c;z)*f(z) be the Hohlov operator defined on the class A of all normalized analytic functions. We determine conditions on the parameters a,b,c such that I_a,b;c(f) will be in the class of parabolic starlike functions S_p(α,β). Our results extend several earlier results.

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Paper's Title:

Boundedness for Vector-Valued Multilinear Singular Integral Operators on Triebel-Lizorkin Spaces

Author(s):

Liu Lanzhe

College of Mathematics
Changsha University of Science and Technology,
Changsha 410077,
P.R. of China.
lanzheliu@263.net

Abstract:

In this paper, the boundedness for some vector-valued multilinear operators associated to certain fractional singular integral operators on Triebel-Lizorkin space are obtained. The operators include Calderón-Zygmund singular integral operator and fractional integral operator.

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Paper's Title:

Differential Sandwich Theorems for Some Subclasses of Analytic Functions

Author(s):

T. N. Shanmugam, V. Ravichandran and S. Sivasubramanian

Department of Mathematics, College of Engineering,
Anna university, Chennai 600 025,
India
shan@annauniv.edu
URL: http://www.annauniv.edu/shan

School of Mathematical Sciences,
Universiti Sains Malaysia,
11800 USM Penang,
Malaysia
vravi@cs.usm.my
URL: http://cs.usm.my/~vravi

Department of Mathematics, Easwari Engineering college,
Ramapuram, Chennai 600 089,
India
sivasaisastha@rediffmail.com

Abstract:

Let and be univalent in with We give some applications of first order differential subordination and superordination to obtain sufficient conditions for normalized analytic function with to satisfy

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Paper's Title:

General Extension of Hardy-Hilbert's Inequality (I)

Author(s):

W. T. Sulaiman

College of Computer Science and Mathematics, University of Mosul,
Iraq.
waadsulaiman@hotmail.com

Abstract:

A generalization for Hardy-Hilbert's inequality that extends the recent results of Yang and Debnath [6], is given.

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Paper's Title:

Distortion Theorems for Certain Analytic Functions Involving the Coefficient Inequalities

Author(s):

Shigeyoshi Owa and Junichi Nishiwaki

Department of Mathematics, Kinki University,
Higashi-Osaka, Osaka 577-8502,
Japan

Abstract:

By virtue of the coefficient inequalities for certain analytic functions in the open unit disk two subclasses and are introduced. The object of the present paper is to discuss the distortion thorems of functions belonging to the classes involving the coefficient inequalities.

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Paper's Title:

A New Family of Periodic Functions as Explicit Roots of a Class of Polynomial Equations

Author(s):

M. Artzrouni

Department of Mathematics, University of Pau
64013 Pau Cedex
Pau, France
marc.artzrouni@univ-pau.fr
URL: http://www.univ-pau.fr/~artzroun

Abstract:

For any positive integer n a new family of periodic functions in power series form and of period n is used to solve in closed form a class of polynomial equations of order n. The n roots are the values of the appropriate function from that family taken at 0, 1, ... , n-1.

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Paper's Title:

A Strengthened Hardy-Hilbert's Type Inequality

Author(s):

Weihong Wang and Bicheng Yang

Department of Mathematics, Guangdong Education Institute,
Guangzhou, Guangdong 520303,
People's Republic Of China
wwh@gdei.edu.cn
bcyang@pub.guangzhou.gd.cn
URL: http://www1.gdei.edu.cn/yangbicheng/index.html

Abstract:

By using the improved Euler-Maclaurin's summation formula and estimating the weight coefficient, we give a new strengthened version of the more accurate Hardy-Hilbert's type inequality. As applications, a strengthened version of the equivalent form is considered.

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Paper's Title:

Salagean-type Harmonic Univalent Functions with Respect to Symmetric Points

Author(s):

R. A. Al-Khal and H. A. Al-Kharsani

Department of Mathematics, Faculty of Science, Girls College,
P.O. Box 838,
Dammam, Saudi Arabia
ranaab@hotmail.com
hakh@hotmail.com

Abstract:

A necessary and sufficient coefficient are given for functions in a class of complex-valued harmonic univalent functions of the form f=h+\g using Salagean operator where h and g are analytic in the unit disk U = {z:|z|<1}. Furthermore, distortion theorems, extreme points, convolution condition, and convex combinations for this family of harmonic functions are obtained.

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Paper's Title:

Necessary and Sufficient Conditions for Uniform Convergence and Boundedness of a General Class of Sine Series

Author(s):

Laszlo Leindler

Bolyai Institute, University of Szeged,
Aradi Vértanúk tere 1,
H-6720 Szeged,
Hungary.
leindler@math.u-szeged.hu

Abstract:

For all we know theorems pertaining to sine series with coefficients from the class γGBVS give only sufficient conditions. Therefore we define a subclass of γGBVS in order to produce necessary and sufficient conditions for the uniform convergence and boundedness if the coefficients of the sine series belong to this subclass; and prove two theorems of this type.

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Paper's Title:

A Coefficient Inequality For Certain Subclasses of Analytic Functions Related to Complex Order

Author(s):

B. Srutha Keerthi, B. Adolf Stephen and S. Sivasubramanian

Department Of Applied Mathematics, Sri Venkateswara College Of Engineering, Anna University,
Sriperumbudur, Chennai - 602 105,
India.
laya@svce.ac.in

Department of Mathematics, Madras Christian College, Chennai - 600059,
India
adolfmcc2003@yahoo.co.in

Department of Mathematics, College of Engineering, Anna University,
Tamilnadu, Chennai - 600 025,
India.
sivasaisastha@rediffmail.com

Abstract:

In this present investigation, the authors obtain coefficient inequality for certain normalized analytic functions of complex order f(z) defined on the open unit disk for which ( and be a complex number) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions of complex order defined by convolution are given. As a special case of this result, coefficient inequality for a class of functions defined through fractional derivatives is obtained. The motivation of this paper is to give a generalization of the coefficient inequalities of the subclasses of starlike and convex functions of complex order.

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Paper's Title:

Generalizations of Hermite-Hadamard's Inequalities for Log-Convex Functions

Author(s):

Ai-Jun Li

School of Mathematics and Informatics, Henan Polytechnic University,
Jiaozuo City, Henan Province,
454010, China.
liaijun72@163.com

Abstract:

In this article, Hermite-Hadamard's inequalities are extended in terms of the weighted power mean and log-convex function. Several refinements, generalizations and related inequalities are obtained.

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Paper's Title:

Oscillation and Boundedness of Solutions to First and Second Order Forced Dynamic Equations with Mixed Nonlinearities

Author(s):

Ravi P. Agarwal and Martin Bohner

Department of Mathematical Sciences, Florida Institute of Technology
Melbourne, FL 32901,
U.S.A.
bohner@mst.edu
URL:http://web.mst.edu/~bohner

Department of Economics and Finance, Missouri University of Science and Technology
Rolla, MO 65401,
U.S.A.
agarwal@fit.edu

Abstract:

Some oscillation and boundedness criteria for solutions to certain first and second order forced dynamic equations with mixed nonlinearities are established. The main tool in the proofs is an inequality due to Hardy, Littlewood and Pólya. The obtained results can be applied to differential equations, difference equations and q-difference equations. The results are illustrated with numerous examples.

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Paper's Title:

Reverses of the CBS Integral Inequality in Hilbert Spaces and Related Results

Author(s):

I. Brnetić, S. S. Dragomir, R. Hoxha and J. Pečarić

Department of Applied Mathematics, Faculty of Electrical Engineering and Computing,
University of Zagreb, Unska 3, 10 000 Zagreb,
Croatia
andrea@zpm.fer.hr

School of Computer Science & Mathematics, Victoria University
Po Box 14428, Melbourne Vic 8001
Australia
sever.dragomir@vu.edu.au
URL:http://rgmia.vu.edu.au/dragomir

Faculty of Applied Technical Sciences, University of Prishtina,
Mother Theresa 5, 38 000 Prishtina
Kosova
razimhoxha@yahoo.com

Faculty of Textile Technology, University of Zagreb,
Pierottijeva 6, 10000 Zagreb,
Croatia
pecaric@hazu.hr

Abstract:

There are many known reverses of the Cauchy-Bunyakovsky-Schwarz (CBS) inequality in the literature. We obtain here a general integral inequality comprising some of those results and also provide other related inequalities. The discrete case, which is of interest in its own turn, is also analysed.

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Paper's Title:

Neighborhoods of Certain Subclasses of Analytic Functions of Complex Order with Negative Coefficients

Author(s):

B. Srutha Keerthi, B. Adolf Stephen, A. Gangadharan, and S. Sivasubramanian

Department of Applied Mathematics,
Sri Venkateswara College of Engineering,
Sriperumbudur, Chennai - 602105,
India.
sruthilaya06@yahoo.co.in

Department of Mathematics,
Madras Christian College,
Chennai - 600059,
India
adolfmcc2003@yahoo.co.in

Department of Applied Mathematics,
Sri Venkateswara College of Engineering,
Sriperumbudur, Chennai - 602105,
India.
ganga@svce.ac.in

Department of Mathematics,
Easwari Engineering College,
Ramapuram, Chennai - 600089,
 India
sivasaisastha@rediffmail.com

Abstract:

The main object of this paper is to prove several inclusion relations associated with the (n, δ) neighborhoods of various subclasses of convex functions of complex order by making use of the known concept of neighborhoods of analytic functions.

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Paper's Title:

Uniqueness of Meromorphic Functions and Weighted Sharing

Author(s):

Indrajit Lahiri and Rupa Pal

Department of Mathematics, University of
Kalyani, West Bengal 741235, India
indr9431@dataone.in

 Jhargram Raj College,
Jhargram, Midnapur(W),
West Bengal 721507,
India
rupa.a.pal@gmail.com

Abstract:

With the help of the notion of weighted sharing of values, we prove a result on uniqueness of meromorphic functions and as a consequence we improve a result of P. Li

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Paper's Title:

Solution of One Conjecture on Inequalities with Power-Exponential Functions.

Author(s):

Seiichi Manyama

Graduate School of Science

 Osaka University

Japan
 manchanr4@gmail.com
 

Abstract:

In this paper, we prove the open inequality a^ea+b^eb≥ a^eb+b^ea for all positive real numbers a and b.

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Paper's Title:

SEVERAL q-INTEGRAL INEQUALITIES

Author(s):

W. T. Sulaiman

Department of Computer Engineering,
College of Engineering,
University of Mosul,
Iraq.

 waadsulaiman@hotmail.com
 

Abstract:

In the present paper several q-integral inequalities are presented, some of them are new and others are generalizations of known results.

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Paper's Title:

On the Degree of Approximation of Continuous Functions that Pertains to the Sequence-To-Sequence Transformation

Author(s):

Xhevat Z. Krasniqi

University of Prishtina,
Department of Mathematics and Computer Sciences,
5 Mother Teresa Avenue, Prishtinë, 10000,
Republic of Kosovo.
 

xheki00@hotmail.com

Abstract:

In this paper we prove analogous theorems like Leindler's 3 using the so-called A-transform of the B-transform of the partial sums of Fourier series. In addition, more than two such transforms are introduced and for them analogous results are showed as well.

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Paper's Title:

Some Remarks on a Result of Bougoffa

Author(s):

James A. Oguntuase, Lars-Erik Persson and Josip E. Pečarič

Department of Mathematics,University of Agriculture,
 P M B 2240, Abeokuta, Nigeria

Department of Mathematics, Luleå University of Technology,
SE-971 87, Luleå , Sweden

Faculty of Textile Technology, University of Zagreb,
Pierottijeva 6, 10000 Zagreb, Croatia
 
oguntuase@yahoo.com, larserik@sm.luth.se, pecaric@hazu.hr.
 

Abstract:

Some new generalizations of the result of L. Bougoffa [J. Inequal. Pure Appl. Math. 7 (2) (2006), Art. 60] are derived and discussed.
 

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Paper's Title:

On a Hilbert-type Inequality with the Polygamma Function

Author(s):

Bing He and Bicheng Yang
Department of Mathematics, Guangdong Education College,
Guangzhou, 510303,
 China.

hzs314@163.com

Department of Mathematics, Guangdong Education College,
Guangzhou, 510303,
 China.

bcyang@pub.guangzhou.gd.cn

 

Abstract:

By applying the method of weight function and the technique of real analysis, a Hilbert-type inequality with a best constant factor is established, where the best constant factor is made of the polygamma function. Furthermore, the inverse form is given.

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Paper's Title:

A New Property of General Means of Order p with an Application to the Theory of Economic Growth

Author(s):

Olivier de La Grandville

 Department of Management Science and Engineering,
Huang Engineering Center, Stanford University,
475 Via Ortega, Stanford, California 94305
U.S.A.

lagrandvil@aol.com

 

Abstract:

The purpose of this note is to demonstrate a new property of the general mean of order p of m ordered positive numbers . If p < 0 and if , the elasticity of with respect to x_m, defined by , tends towards zero, and therefore . This property is then applied to optimal growth theory.

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Paper's Title:

Good and Special Weakly Picard Operators for the Stancu Operators with Modified Coefficients

Author(s):

Loredana-Florentina Galea and Alexandru-Mihai Bica

The Agora University of Oradea,
Piata Tineretului no. 8,
410526, Oradea,
Romania

University of Oradea,
Str. Universitatii No. 1,
410087, Oradea,
Romania

loredana.galea@univagora.ro
smbica@yahoo.com
abica@uoradea.ro

 

Abstract:

In this paper some properties of good and special weakly Picard operators for the Stancu operators with modified coefficients are obtained. In the study of the sequence of iterates of these operators, we obtain the property of dual monotone iteration.

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Paper's Title:

On the Inequality with Power-Exponential Function

Author(s):

Seiichi Manyama

Graduate School of Science

 Osaka University

Japan
 manchanr4@gmail.com
 

Abstract:

In this paper, we prove the inequality < for 0<a<b. Other related conjectures are also presented.

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Paper's Title:

On the Boundedness of Hardy's Averaging Operators

Author(s):

Dah-Chin Luor

Department of Applied Mathematics,
I-Shou University, Dashu District,
Kaohsiung City 84001,
Taiwan, R.O.C.
dclour@isu.edu.tw

Abstract:

In this paper we establish scales of sufficient conditions for the boundedness of Hardy's averaging operators on weighted Lebesgue spaces. The estimations of the operator norms are also obtained. Included in particular are the Erdélyi-Kober operators.

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Paper's Title:

New Solutions to Non-Smooth PDEs

Author(s):

Moawia Alghalith

University of the West Indies,
St. Augustine,
Trinidad

moawia.alghalith@sta.uwi.edu

Abstract:

We provide strong solutions to partial differential equations when the function is non-differentiable.

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Paper's Title:

A Short Proof of an Open Inequality with Power-Exponential Functions

Author(s):

Mitsuhiro Miyagi and Yusuke Nishizawa

General Education, Ube National College of Technology,
Tokiwadai 2-14-1, Ube,
Yamaguchi 755-8555,
Japan

E-mail: miyagi@ube-k.ac.jp   
yusuke@ube-k.ac.jp  

Abstract:

V. Cîrtoaje conjectured that a^3b + b^3a + ( (a -b)/2 )⁴ ≤ 2 holds for all nonnegative numbers a and b with a +b =2. In this short note, we give a proof of the Cîrtoaje's conjecture with power-exponential functions.

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Paper's Title:

A_p Functions and Maximal Operator

Author(s):

Chunping Xie

Department of Mathematics,
Milwaukee School of Engineering,
1025 N. Broadway,
Milwaukee, Wisconsin 53202,
U. S. A.

E-mail: xie@msoe.edu

URL: http://www.msoe.edu/people/chunping.xie

Abstract:

The relationship between A_p functions and Hardy-Littlewood maximal operator on L^p,λ(w), the weighted Morrey space, has been studied. Also the extropolation theorem of L^p,λ(w) has been considered.

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Paper's Title:

On a Problem on Periodic Functions

Author(s):

Adel A. Abdelkarim

Mathematics Department, Faculty of Science,
Jerash Private University, Jerash,
Jordan.

E-mail: adelafifo_afifo@yahoo.com
 

Abstract:

Given a continuous periodic real function f with n translates  f₁ ,..., f_n , where f_i(x)=f(x+a_i), i=1,...,n. We solve a problem by Erdos and Chang and show that there are rational numbers r,s such that f(r)≥ f_i(r), f(s)≤ f_i(s), i=1,...,n. No restrictions on the constants or any further restriction on the function f are necessary as was imposed earlier.

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Paper's Title:

On Eigenvalues and Boundary Curvature of the C*-algebra Numerical Rang

Author(s):

M. T. Heydari

Department of Mathematics,
College of Sciences,
Yasouj University,
Yasouj, 75914-74831,
Iran.

E-mail: heydari@yu.ac.ir 

Abstract:

Let A be a C*-algebra with unit 1 and a∈A be a nilpotent. By Donoghue's Theorem, all corner points of its numerical range V(a) belong to the spectrum σ(a). It is therefore natural to expect that, more generally, the distance from a point p on the boundary ∂ V(a) of V(a) to σ(a) should be in some sense bounded by the radius of curvature of ∂ V(a) at p.

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Paper's Title:

Some properties of quasinormal, paranormal and 2-k^* paranormal operators

Author(s):

Shqipe Lohaj

Department of Mathematics,
University of Prishtina,
10000, Kosova.
E-mail: shqipe.lohaj@uni-pr.edu

Abstract:

In the beginning of this paper some conditions under which an operator is partial isometry are given. Further, the class of 2-k^* paranormal operators is defined and some properties of this class in Hilbert space are shown. It has been proved that an unitarily operator equivalent with an operator of a 2-k^* paranormal operator is a 2-k^* paranormal operator, and if is a 2-k^* paranormal operator, that commutes with an isometric operator, then their product also is a $2-k^*$ paranormal operator.

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Paper's Title:

On the Polyconvolution of Hartley Integral Transforms H₁, H₂, H₁ and Integral Equations

Author(s):

Nguyen Minh Khoa and Dau Xuan Luong

Department of Mathematics,
Electric Power University,
Ha Noi, and Faculty of Fundamental Science,
Ha Long University, Quang Ninh,
Viet Nam.
E-mail: khoanm@epu.edu.vn, dauxuanluong@gmail.com 

Abstract:

In this paper, we construct and study a new polyconvolution * (f,g,h)(x) of functions f, g, h. We will show that the polyconvolution satisfy the following factorization equality

H₁[*(f,g,h)](y)=(H₂f)(y)(H₁g)(y)(H₁h)(y), ∀y∈ R. 

We prove the existence of this polyconvolution in the space L(R). As examples, applications to solve an integral equation of polyconvolution type and two systems of integral equations of polyconvolution type are presented.

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Paper's Title:

Structural and Spectral Properties of k-Quasi Class Q Operators

Author(s):

Valdete Rexhëbeqaj Hamiti and Shqipe Lohaj

Department of Mathematics,
Faculty of Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000,
Kosova.
E-mail: valdete.rexhebeqaj@uni-pr.edu

Department of Mathematics,
Faculty of Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000,
Kosova.
E-mail: shqipe.lohaj@uni-pr.edu

Abstract:

An operator is said to be k-quasi class Q if , for all where k is a natural number. In this paper, first we will prove some results for the matrix representation of k-quasi class Q operators. Then, we will give the inclusion of approximate point spectrum of k-quasi class Q operators. Also, we will give the equivalence between Aluthge transformation and *-Aluthge transformation of k-quasi class Q operators.

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Paper's Title:

Some Properties of Cosine Series with Coefficients from Class of General Monotone Sequences Order r

Author(s):

Corina Karim, Moch. Aruman Imron

Department of Mathematics,
Universitas Brawijaya,
Indonesia.
E-mail: co_mathub@ub.ac.id
maimr@ub.ac.id

Abstract:

The coefficient of sine series from general monotone class has been generalized by Bogdan Szal to the new class which is called class of general monotone order r. This coefficient class is more general than class of general monotone introduced by Tikhonov. By special case, we study properties of cosine series with coefficient of sine series from the class of general monotone order r.

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Paper's Title:

Rational Expressions of Arithmetic and Geometric Means for the Sequence n^p_{n ∈ N} and the Geometric Progression

Author(s):

M. Kinegawa, S. Miyamoto and Y. Nishizawa

Faculty of Education, Saitama University,
Shimo-okubo 255, Sakura-ku, Saitama-city, Saitama,
Japan.
E-mail: m.kinegawa.645@ms.saitama-u.ac.jp
 
Faculty of Education, Saitama University,
Shimo-okubo 255, Sakura-ku, Saitama-city, Saitama,
Japan.
E-mail: s.miyamoto.245@ms.saitama-u.ac.jp

Faculty of Education, Saitama University,
Shimo-okubo 255, Sakura-ku, Saitama-city, Saitama,
Japan.
E-mail: ynishizawa@mail.saitama-u.ac.jp

Abstract:

In this paper, we consider the arithmetic and geometric means for the sequence n^p_{n ∈ N} and the geometric progression. We obtain the results associated with the rational expressions of the means.

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Paper's Title:

Pointwise Convergence of Fourier-type Series with Exponential Weights

Author(s):

Hee Sun Jung and Ryozi Sakai

Department of Mathematics Education, Sungkyunkwan University,
Seoul 110-745,
Republic of Korea.
E-mail: hsun90@skku.edu

Department of Mathematics,
Meijo University, Nagoya 468-8502,
Japan.
E-mail: ryozi@hm.aitai.ne.jp

Abstract:

Let R = ( - ∞,∞), and let Q∈C¹(R):R→[0,∞) be an even function. We consider the exponential weights w(x)=e^-Q(x), x∈R. In this paper we obtain a pointwise convergence theorem for the Fourier-type series with respect to the orthonormal polynomials {p_n(w²;x)}.

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Paper's Title:

Corrigendum for A Review on Minimally Supported Frequency Wavelets

Author(s):

K Pallavi¹, M C Lineesh¹, A Noufal²

¹Department of Mathematics,
National Institute of Technology Calicut,
Kerala 673601,
India.
E-mail:  pavikrishnakumar@gmail.com
lineesh@nitc.ac.in

²Department of Mathematics,
Cochin University of Science and Technology,
Kerala 682022,
India.
E-mail: noufal@cusat.ac.in

Abstract:

This article is a corrigendum to AJMAA Volume 18, Issue 2, Article 17, {PDF Link}.

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Paper's Title:

Three Inequalities Associated with Rado Inequality

Author(s):

Rin Miyao, Yusuke Nishizawa, Keigo Takamura

Faculty of Education,
Saitama University,
Shimo-okubo 255, Sakura-ku, Saitama-city, Saitama,
Japan.
E-mail: r.miyao.242@ms.saitama-u.ac.jp

Faculty of Education,
Saitama University,
Shimo-okubo 255, Sakura-ku, Saitama-city, Saitama,
Japan.
E-mail: ynishizawa@mail.saitama-u.ac.jp

Faculty of Education,
Saitama University,
Shimo-okubo 255, Sakura-ku, Saitama-city, Saitama,
Japan.
E-mail: k.takamura.442@ms.saitama-u.ac.jp

Abstract:

In this short note we estimate three inequalities associated with Rado inequality and show the refinement and reverse of Arithmetic mean- Geometric mean inequality.

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Paper's Title:

Boundness of the Power Exponential Function a^2b +b^2a

Author(s):

Yusuke Nishizawa, Yukuhito Yasuda

Faculty of Education, Saitama University,
Shimo-okubo 255, Sakura-ku, Saitama-city, Saitama,
Japan.
E-mail: ynishizawa@mail.saitama-u.ac.jp 

Faculty of Education, Saitama University,
Shimo-okubo 255, Sakura-ku, Saitama-city, Saitama,
Japan.
E-mail: y.yasuda.694@ms.saitama-u.ac.jp
 

Abstract:

In this paper, we consider the boundness of the power exponential function a^2b +b^2a for nonnegative real numbers a and b. The author proved that the function has the maximum value 1 for a + b = ½, but it is no known that the minimum value for a + b = ½. In this paper, we give the new proof of the function has the maximum value 1 and show that a^2b +b^2a > 0.989905 for a + b = ½.

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Paper's Title:

Inequalities Involving A_∞ Weights by Extrapolations

Author(s):

Chunping Xie

Mathematics Department,
Milwaukee School of Engineering,
1025 N. Broadway,
Milwaukee, Wisconsin 53202,
U.S.A.
E-mail: xie@msoe.edu
URL: https://www.msoe.edu/directory/profile/chunping.xie/

Abstract:

We generalize the extrapolation theorem from A_p weights to A_∞ weights on the setting of weighted Morrey spaces by using the Rubio de Francia algorithm and ideas in a paper by D. Cruz-Uribe et al. First we have proved the classical Hardy-Littlewood maximal operator is bounded on the weighted Morrey spaces if the weight w(x) is in A_∞ and then we have obtained inequalities involving the maximal operator, vector-valued maximal operator, the sharp maximal operator, and A_∞ weights.

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Paper's Title:

Using an Euler Type Transform for Accelerating Convergence of Series

Author(s):

Nimete Sh. Berisha, Faton M. Berisha^*, Murat Sadiku

Faculty of Economics, University of Prishtina,
Agim Ramadani st., 10000 Pristina,
Kosovo.
E-mail: nimete.berisha@uni-pr.edu
URL: https://staff.uni-pr.edu/profile/nimeteberisha

Faculty of Mathematics and Sciences, University of Prishtina,
Mother Teresa st., 10000 Pristina,
Kosovo.
E-mail: faton.berisha@uni-pr.edu
URL: https://staff.uni-pr.edu/profile/fatonberisha

Faculty of Business Administration,
South East European University,
Tetovo,
North Macedonia.
E-mail: m.sadiku@seeu.edu.mk

Abstract:

In the paper we give a property of an operator of generalised difference, defined earlier, linear on a set of sequences, and use it to establish Euler type transforms for alternating series. These transforms accelerate the convergence of series under the same conditions as the transforms of non-alternating series. We also give analysis of an algorithm for computing a partial sum of the transformed series by using a higher order operator of generalised difference, and prove a theorem stating its order of complexity.

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1: Paper Source PDF document

Paper's Title:

On the Integral Equations via Hartley Superconvolutions

Author(s):

Nguyen Minh Khoa

Department of Mathematics, Electric Power University,
Ha Noi,
Viet Nam.
E-mail: khoanm@epu.edu.vn

Abstract:

The new superconvolutions for the Hartley integral transforms are formulated and their properties are studied. Furthermore, we also formulate the Young type theorem for these superconvolutions in the function space L_s^αβγ(R) and get its norm estimations. We apply them to solve integral equations and system of integral equations of Toeplitz plus Hankel type.

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