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117: Paper Source PDF document

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,
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} = |xn|-yn-b and y{n+1} = xn - |yn| + 1 where n 0 and b6. 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.

83: Paper Source PDF document

Paper's Title:

Applications of Relations and Relators in the Extensions of Stability Theorems for Homogeneous and Additive Functions

Author(s):

Árpád Száz

Institute of Mathematics, University of Debrecen,
H-4010 Debrecen, Pf. 12,
Hungary
szaz@math.klte.hu

Abstract:

By working out an appropriate technique of relations and relators and extending the ideas of the direct methods of Z. Gajda and R. Ger, we prove some generalizations of the stability theorems of D. H. Hyers, T. Aoki, Th. M. Rassias and P. Găvruţă in terms of the existence and unicity of 2-homogeneous and additive approximate selections of generalized subadditive relations of semigroups to vector relator spaces. Thus, we obtain generalizations not only of the selection theorems of Z. Gajda and R. Ger, but also those of the present author.

63: Paper Source PDF document

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.

60: Paper Source PDF document

Paper's Title:

Ostrowski Type Inequalities for Lebesgue Integral: a Survey of Recent Results

Author(s):

Sever S. Dragomir1,2

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:

The main aim of this survey is to present recent results concerning Ostrowski type inequalities for the Lebesgue integral of various classes of complex and real-valued functions. The survey is intended for use by both researchers in various fields of Classical and Modern Analysis and Mathematical Inequalities and their Applications, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.

48: Paper Source PDF document

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.

42: Paper Source PDF document

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.

42: Paper Source PDF document

Paper's Title:

Inequalities for Discrete F-Divergence Measures: A Survey of Recent Results

Author(s):

Sever S. Dragomir1,2

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:

In this paper we survey some recent results obtained by the author in providing various bounds for the celebrated f-divergence measure for various classes of functions f. Several techniques including inequalities of Jensen and Slater types for convex functions are employed. Bounds in terms of Kullback-Leibler Distance, Hellinger Discrimination and Varation distance are provided. Approximations of the f-divergence measure by the use of the celebrated Ostrowski and Trapezoid inequalities are obtained. More accurate approximation formulae that make use of Taylor's expansion with integral remainder are also surveyed. A comprehensive list of recent papers by several authors related this important concept in information theory is also included as an appendix to the main text.

37: 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.

32: 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.

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.

28: Paper Source PDF document

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.

27: Paper Source PDF document

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 ym(x)=fm(x)+∫ax Km(x, t)ym(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-∫0tK(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,..., Ln which can be obtained by means of K and some inequalities among the functions f, h2, h3,..., hi for i=2, 3,...., n are satisfied on the infinite interval [0, ∞), where hi is the solution of the equation hi(t)=1-Li* hi and n is a natural number.

26: Paper Source PDF document

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.

25: 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

Quito,
E-mail: borys_yamil@yahoo.com, balvarez@uce.edu.ec

Escuela de Ciencias Fisicas y Matematica
Facultad de Ciencias Exactas y Naturales
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.

25: Paper Source PDF document

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,
E-mail: jmaxwellcampbell@gmail.com

Department of Mathematics, University of Taipei,
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.

25: Paper Source PDF document

Paper's Title:

A Unifying View of Some Banach Algebras

Author(s):

R. Kantrowitz

Mathematics & Statistics Department,
Hamilton College,
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.

24: Paper Source PDF document

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 .

23: Paper Source PDF document

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.

22: Paper Source PDF document

Paper's Title:

A Note on Schur's Lemma in Banach Function Spaces

Author(s):

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

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

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.

21: Paper Source PDF document

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.

21: Paper Source PDF document

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.

20: Paper Source PDF document

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.

19: Paper Source PDF document

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.

19: Paper Source PDF document

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,
Universitŕ di Salerno,
Via Ponte Don Melillo, 84084 Fisciano (Sa),
Italy
manzo@diima.unisa.it

Department of Technical Cybernetics,
Dnipropetrovsk Technical University,
Dnipro
petrovsk,
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.

19: Paper Source PDF document

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.

19: Paper Source PDF document

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.

19: Paper Source PDF document

Paper's Title:

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

Author(s):

Steven G. From

Department of Mathematics

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.

19: Paper Source PDF document

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.

18: Paper Source PDF document

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,
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.

17: Paper Source PDF document

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.

17: Paper Source PDF document

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.

17: Paper Source PDF document

Paper's Title:

Para-chaotic Tuples of Operators

Author(s):

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

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.

17: Paper Source PDF document

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,
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.

17: Paper Source PDF document

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.

17: Paper Source PDF document

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.

17: 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  Sp  spaces.

17: Paper Source PDF document

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.

16: Paper Source PDF document

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.

16: Paper Source PDF document

Paper's Title:

Expected Utility with Subjective Events

Author(s):

Jacob Gyntelberg and Frank Hansen

Bank for International Settlements,
Basel,
Switzerland

jacob.gyntelberg@bis.org

Tohoku University, Institute for International Education,
Sendai,
Japan

frank.hansen@m.tohoku.ac.jp

Abstract:

We provide a new theory of expected utility with subjective events modeled by a lattice of projections. This approach allows us to capture the notion of a small world'' as a context dependent or local state space embedded into a subjective set of events, the grand world''. For each situation the decision makers' subjective small world'' reflects the events perceived to be relevant for the act under consideration. The subjective set of events need not be representable by a classical state space. Maintaining preference axioms similar in spirit to the classical axioms, we obtain an expected utility representation which is consistent across local state spaces and separates subjective probability and utility. An added benefit is that this alternative expected utility representation allows for an intuitive distinction between risk and uncertainty.

16: Paper Source PDF document

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.

16: Paper Source PDF document

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 δB(X) and ρB(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 δB(X), ρB(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.

15: Paper Source PDF document

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.

15: Paper Source PDF document

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).

15: Paper Source PDF document

Paper's Title:

Error Estimates for Approximations of the Laplace transform of Functions in Lp 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 Lp 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.

15: Paper Source PDF document

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 RN. Two kinds of growth are considered: the Bloch--type growth and growth conditions expressed through integrals involving involutions of the unit ball.

15: Paper Source PDF document

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.

15: Paper Source PDF document

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.

15: Paper Source PDF document

Paper's Title:

Topological Aspects of Discrete Switch Dynamical Systems

Author(s):

Faiz Imam and Sharan Gopal

Department of Mathematics,
India.
E-mail: mefaizy@gmail.com

Department of Mathematics,
India.
E-mail: sharanraghu@gmail.com

Abstract:

14: Paper Source PDF document

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.

14: Paper Source PDF document

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.

14: Paper Source PDF document

Paper's Title:

Local and Global Existence and Uniqueness Results for Second and Higher Order Impulsive Functional Differential Equations with Infinite Delay

Author(s):

Johnny Henderson and Abdelghani Ouahab

Department of Mathematics, Baylor University,
Waco, Texas 76798-7328
USA.
Johnny_Henderson@baylor.edu

Laboratoire de Mathématiques, Université de Sidi Bel Abbés
BP 89, 22000 Sidi Bel Abbées,
Algérie.
ouahab@univ-sba.dz

Abstract:

In this paper, we discuss the local and global existence and uniqueness results for second and higher order impulsive functional differential equations with infinite delay. We shall rely on a nonlinear alternative of Leray-Schauder. For the global existence and uniqueness we apply a recent Frigon and Granas nonlinear alternative of Leray-Schauder type in Fréchet spaces.

14: Paper Source PDF document

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

Universitŕ 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.

14: Paper Source PDF document

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.

14: Paper Source PDF document

Paper's Title:

Application of Equivalence Method to Classify Monge-Ampčre 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-Ampčre equations of elliptic type. Then we find a necessary and sufficient conditions such that a Monge-Ampčre equation is either contactomorphic to the Laplace equation or to an Euler-Lagrange equation.

14: Paper Source PDF document

Paper's Title:

Existence, Global Regularity and Uniqueness of Solutions of the Navier-Stokes Equations in Space Dimension 3 when the Initial Data are Regular

Author(s):

Moulay D. Tidriri

Email: mtctyasa@gmail.com

Abstract:

The existence, regularity, and uniqueness of global solutions of the Navier-Stokes equations in are given for when the initial velocity for all integers q0 and div u0 = 0.

14: 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].

13: Paper Source PDF document

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 Đ be a convex quadrilateral in the plane and let M1 and M2 be the midpoints of the diagonals of Đ. It is well–known that if E is an ellipse inscribed in Đ, 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 Đ. This completely characterizes the locus of centers of ellipses inscribed in Đ. We also show that there is a unique ellipse of maximal area inscribed in Đ. Finally, we prove our most signifigant results: There is a unique ellipse of minimal eccentricity inscribed in Đ.

13: Paper Source PDF document

Paper's Title:

Scope of the Logarithmic Mean

Author(s):

Murali Rao and Agnish Dey

Department of Mathematics,
University of Florida,
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.

13: Paper Source PDF document

Paper's Title:

Polyanalytic Functions on Subsets of Z[i]

Author(s):

Abtin Daghighi

SE-581 83,
Sweden.

E-mail: abtindaghighi@gmail.com

Abstract:

For positive integers q we consider the kernel of the powers Lq 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.

12: Paper Source PDF document

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.

12: Paper Source PDF document

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

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 χ2divergence, 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.

12: Paper Source PDF document

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.

12: Paper Source PDF document

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.

12: Paper Source PDF document

Paper's Title:

Hyperbolic Barycentric Coordinates

Author(s):

Abraham A. Ungar

Department of Mathematics, North Dakota State University,
Fargo, ND 58105,
USA
Abraham.Ungar@ndsu.edu
URL
: http://math.ndsu.nodak.edu/faculty/ungar/

Abstract:

A powerful and novel way to study Einstein's special theory of relativity and its underlying geometry, the hyperbolic geometry of Bolyai and Lobachevsky, by analogies with classical mechanics and its underlying Euclidean geometry is demonstrated. The demonstration sets the stage for the extension of the notion of barycentric coordinates in Euclidean geometry, first conceived by Möbius in 1827, into hyperbolic geometry. As an example for the application of hyperbolic barycentric coordinates, the hyperbolic midpoint of any hyperbolic segment, and the centroid and orthocenter of any hyperbolic triangle are determined.

12: Paper Source PDF document

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 Tφf=P(φf) where P is the projection from L2(β) onto H2(β) and the symbol φ ∈ L2(β) for a given sequence β=‹βnn∈ 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.

12: Paper Source PDF document

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, EI, inscribed in a parallelogram, Đ. We also prove that the smallest nonnegative angle between equal conjugate diameters of $EI equals the smallest nonnegative angle between the diagonals of Đ. We also prove that if EM is the unique ellipse inscribed in a rectangle, R, which is tangent at the midpoints of the sides of R, then EM is the unique ellipse of minimal eccentricity, maximal area, and maximal arc length inscribed in R. Let Đ be any convex quadrilateral. In previous papers, the author proved that there is a unique ellipse of minimal eccentricity, EI, inscribed in Đ, and a unique ellipse, EO, of minimal eccentricity circumscribed about Đ. We defined Đ to be bielliptic if EI and EO have the same eccentricity. In this paper we show that a parallelogram, Đ, is bielliptic if and only if the square of the length of one of the diagonals of Đ equals twice the square of the length of one of the sides of Đ . 12: Paper Source PDF document 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, texp and tB, 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. 12: Paper Source PDF document 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. 12: Paper Source PDF document 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 EQ1rot 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. 12: 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. 12: Paper Source PDF document Paper's Title: Attempts to Define a Baum--Connes Map Via Localization of Categories for Inverse Semigroups Author(s): Bernhard Burgstaller Departamento de Matematica, Universidade Federal de Santa Catarina, CEP 88.040-900 Florianopolis-SC, Brasil. E-mail: bernhardburgstaller@yahoo.de URL: http://mathematik.work/bernhardburgstaller/index.html Abstract: An induction functor in inverse semigroup equivariant KK-theory is considered, and together with %a restriction functors certain results similar to those known from the Mackey machinery are shown. It is also verified that for any so-called E-continuous inverse semigroup its equivariant KK-theory satisfies the universal property and is a triangulated category. 12: Paper Source PDF document 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. 12: Paper Source PDF document Paper's Title: Coexisting Attractors and Bubbling Route to Chaos in Modified Coupled Duffing Oscillators Author(s): B. Deruni1, A. S. Hacinliyan1,2, 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. 12: Paper Source PDF document 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 Co and (Co,1) semigroup. The work of this paper is inspired by the work in [2] and [6]. 12: Paper Source PDF document 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. 11: Paper Source PDF document 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. 11: Paper Source PDF document 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. 11: Paper Source PDF document Paper's Title: A Note On The Global Behavior Of A Nonlinear System of Difference Equations Author(s): Norman H. Josephy, Mihaela Predescu and Samuel W. Woolford Department of Mathematical Sciences, Bentley University, Waltham, MA 02452, U.S.A. mpredescu@bentley.edu njosephy@bentley.edu swoolford@bentley.edu 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. 11: Paper Source PDF document 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. 11: Paper Source PDF document 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. 11: Paper Source PDF document 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 Fčs, 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. 11: Paper Source PDF document 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. 11: 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. 11: Paper Source PDF document 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]. 10: Paper Source PDF document 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 Podchor ąźych 2, 30-084 Krak ów, 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 10: Paper Source PDF document 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. 10: 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. 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. 10: Paper Source PDF document 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. 10: 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. 10: Paper Source PDF document 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 KPar(S), and we show that the suitable quotient of KPar(S) is a kind of crossed product. 10: Paper Source PDF document 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. 10: Paper Source PDF document Paper's Title: The Functional Equation With an Exponential Polynomial Solution and its Stability Author(s): Young Whan Lee1, Gwang Hui Kim2*, 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: i ghkim@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 pn(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 10: 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. 9: Paper Source PDF document 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, S tn Forces, Kingston, Ontario, Canada K7k 7b4 URL : URL : 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. 9: Paper Source PDF document 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. 9: Paper Source PDF document 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. 9: Paper Source PDF document 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. 9: Paper Source PDF document 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 qth 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. 9: Paper Source PDF document 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 Lp(0,T,W01,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 Lp'(0,T,W-1,p'(Ώ,w*)). 9: Paper Source PDF document 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 Abbčs 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. 9: Paper Source PDF document 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. 9: Paper Source PDF document 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 ,..., fn , where fi(x)=f(x+ai), i=1,...,n. We solve a problem by Erdos and Chang and show that there are rational numbers r,s such that f(r)≥ fi(r), f(s)≤ fi(s), i=1,...,n. No restrictions on the constants or any further restriction on the function f are necessary as was imposed earlier. 9: Paper Source PDF document 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.comrenuanand71@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 = (Mk,l). We also made an attempt to study some topological and algebraic properties of these sequence spaces. 9: Paper Source PDF document 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. 9: Paper Source PDF document 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). 9: Paper Source PDF document 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. 9: 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. 9: Paper Source PDF document 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. 9: Paper Source PDF document 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, Prishtin ë 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 Cesŕro 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. 8: Paper Source PDF document 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 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. 8: Paper Source PDF document 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. 8: Paper Source PDF document 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. 8: Paper Source PDF document 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. 8: Paper Source PDF document 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. 8: Paper Source PDF document 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. 8: Paper Source PDF document 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. 8: Paper Source PDF document 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. 8: Paper Source PDF document 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. 8: Paper Source PDF document 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. 8: Paper Source PDF document 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. 8: Paper Source PDF document 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. 8: Paper Source PDF document 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. 8: Paper Source PDF document 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. 8: Paper Source PDF document 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. 8: Paper Source PDF document 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 RN, NN*. 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. 7: Paper Source PDF document 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. Département de Mathématiques, Université de Perpignan, 66860 Perpignan, France. 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. 7: Paper Source PDF document 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. 7: Paper Source PDF document 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. 7: Paper Source PDF document 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. 7: Paper Source PDF document 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 Tlm([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 Tlm([α1];α,β) . We consider integral operators associated with functions belonging to the class Hlm([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 Tlm([α1];α,β) and we obtain properties associated with generalized fractional calculus operators. 7: Paper Source PDF document 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. 7: Paper Source PDF document Paper's Title: Sharp Lp 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 Abstract: For j=1,...,n, let Ωj be open sets of the complex plane and let φj be holomorphic functions on Ωj such that φj'' does not vanish identically on Ωj. We consider φ(z1,...,zn) =φ1(z1) +...+φn(zn). 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. 7: Paper Source PDF document 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 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 7: Paper Source PDF document 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 BA (H) is said to be (A, k)-quasi-hyponormal if 7: Paper Source PDF document 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. 7: Paper Source PDF document 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. 7: Paper Source PDF document 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. 7: Paper Source PDF document 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. 7: Paper Source PDF document 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. 7: Paper Source PDF document 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. 7: Paper Source PDF document 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. 7: Paper Source PDF document 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. 7: Paper Source PDF document 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. 7: Paper Source PDF document 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. 7: Paper Source PDF document 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. 6: Paper Source PDF document 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. 6: Paper Source PDF document 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, · · · , an, an+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, · · · , an and the coefficients 2(1-cos(π/(2n + 1))) and 2(1 + cos(π/(2n + 1))) are the best possible. 6: Paper Source PDF document 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. 6: Paper Source PDF document 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. 6: Paper Source PDF document 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. 6: Paper Source PDF document 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. 6: Paper Source PDF document 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. 6: Paper Source PDF document 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. 6: 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 p1, 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. 6: Paper Source PDF document Paper's Title: On some Strongly Nonlinear Elliptic Problems in -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 Fčs, 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 Lą(Ώ). 6: Paper Source PDF document 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. 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.. 6: Paper Source PDF document 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 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 6: Paper Source PDF document Paper's Title: Ap 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 Ap functions and Hardy-Littlewood maximal operator on Lp,λ(w), the weighted Morrey space, has been studied. Also the extropolation theorem of Lp,λ(w) has been considered. 6: Paper Source PDF document 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$Qkλ,m,γ by the Hadamard product (or convolution) of two linear operators Dkλ and Im,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:

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:

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:

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:

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:

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

Author(s):

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.

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:

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).

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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:

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:

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.

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:

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,ai,bi,ci,2) to measure the difference between isosceles orthogonality and special Carlsson orthogonalities. At the same time, we also present the geometric constant C(X,ai,bi,ci), 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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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,
K.S.A.
E-mail: ansari.abuzaid@gmail.com, ansari.abuzaid@iu.edu.sa

Department of Mathematics,
Faculty of Science,
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:

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:

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,
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:

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:

Some Approximation for the linear combinations of modified Beta operators

Author(s):

Naokant Deo

Department of Applied Mathematics
Delhi College of Engineering
India.
dr_naokant_deo@yahoo.com

Abstract:

In this paper, we propose a sequence of new positive linear operators βn to study the ordinary approximation of unbounded functions by using some properties of the Steklov means.

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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:

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,
értanúk 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:

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:

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:

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:

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:

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 n2, 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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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:

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:

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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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, Luleĺ University of Technology,
SE-971 87, Luleĺ , 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:

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.

Department of Mathematics, Guangdong Education College,
Guangzhou, 510303,
China.

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:

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 {Tj}Ni=1 of asymptotically quasi Ij-nonexpansive mappings as well as a family of {Ij}Nj=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:

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

Department of Mathematics, Semnan University,
Iran

Divandari@sun.Semnan.ac.ir

Department of Mathematics, Semnan University,
Iran

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:

L∞- Error Estimate of Schwarz Algorithm for Elliptic Quasi-Variational Inequalities Related to Impulse Control Problem

Author(s):

Lab. LANOS, Department of Mathematics,
P.O.Box 12, Annaba 23000,
Algeria.

Lab. LAIG, Department of Mathematics,
University May 8th 1945,
P.O.Box 401, Guelma 24000,
Algeria.

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:

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.

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:

On the Hyers-Ulam Stability of Homomorphisms and Lie Derivations

Author(s):

Department of Mathematics, Payame Noor University,
P.O. Box: 19395-3697, Tehran,
Iran.

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. 5: Paper Source PDF document 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. 5: Paper Source PDF document 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. 5: Paper Source PDF document 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. 5: Paper Source PDF document 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 σkn,n of the Hankel matrix Dn, where kn/n→θ∈[0,1] as n→∞. Moreover, we obtain asymptotics of the Kolmogorov, Gelfand and linear k-widths, k=kn, of the unit ball An,2 of Pn∩L2(Γ) in the space L2(μ,E), where Γ={z:|z|=1} and Pn is the class of all polynomials of the degree at most n. 5: Paper Source PDF document 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 Ak:EE*, k=1, 2, 3 , ... be a family of inverse strongly monotone maps such that k=1 Ak-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. 5: Paper Source PDF document 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 Hs(Rd) are derived. Necessary and sufficient conditions for the sequence of vectors to be tight wavelet frames in Hs(Rd) are obtained. Further, as an application an example of tight wavelet frames for Hs(R2) as bivariate box spline over 3-direction are given. 5: Paper Source PDF document 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. 5: Paper Source PDF document 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, ,Fn 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 5: 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. 5: Paper Source PDF document 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. 5: Paper Source PDF document 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. 5: Paper Source PDF document 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. 5: Paper Source PDF document 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. 5: Paper Source PDF document 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. 5: Paper Source PDF document 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. 5: 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 Gp and Kp on the displacement of the pious is studied numerically at any time tn. 5: Paper Source PDF document 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. 5: Paper Source PDF document 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. 5: Paper Source PDF document 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. 5: Paper Source PDF document 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. 5: Paper Source PDF document 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. 5: Paper Source PDF document 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. 5: 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. 5: Paper Source PDF document 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. 4: Paper Source PDF document 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 4: Paper Source PDF document 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. 4: Paper Source PDF document 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. 4: Paper Source PDF document 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. 4: 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. 4: Paper Source PDF document 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, Universitŕ degli Studi di Napoli "Parthenope", Via Medina, 80133 Napoli, Italy chiara.donnini@uniarthenope.it {Dipartimento di Matematica e Informatica, Universitŕ 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. 4: Paper Source PDF document Paper's Title: On Stan Ulam and his Mathematics Author(s): Krzysztof Ciesielski and Themistocles M. Rassias Mathematics Institute, Jagiellonian University, Ł jasiewicza 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. 4: Paper Source PDF document 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. 4: Paper Source PDF document 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 . 4: Paper Source PDF document 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. 4: Paper Source PDF document 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: XX two Kakutani maps; if for each nonempty finite subset A of D and for any x ∈ coA, F (x) coA ≠ Ř, 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. 4: Paper Source PDF document 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 4: Paper Source PDF document 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. 4: Paper Source PDF document 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. 4: Paper Source PDF document 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. 4: Paper Source PDF document 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. 4: Paper Source PDF document 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 xm, defined by , tends towards zero, and therefore . This property is then applied to optimal growth theory. 4: Paper Source PDF document 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 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. 4: Paper Source PDF document 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. 4: Paper Source PDF document 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]. 4: Paper Source PDF document 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. 4: Paper Source PDF document 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 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 Gλ which was introduced and studied earlier by Silverman [7]. 4: Paper Source PDF document 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 Abstract: Let Ap(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 Cp(n,α,β,λ,μ) of Ap. 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 Cp(n,α,β,λ,μ) 4: Paper Source PDF document 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 S1nc. We examine the K-theory of this algebra and the subalgebras S1nc/Ik, Ik . Where Ik, for each k, is the ideal in S1nc generated by all products of generators hs containing at least k+1 pairwise different generators. Moreover we prove that such algebra divided by the ideal I2 is commutative. 4: Paper Source PDF document 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. 4: Paper Source PDF document 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. 4: Paper Source PDF document 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. 4: Paper Source PDF document 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. 4: Paper Source PDF document 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. 4: Paper Source PDF document 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. 4: Paper Source PDF document 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. 4: Paper Source PDF document 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. 4: Paper Source PDF document 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, Ei=[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. 4: Paper Source PDF document 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. 4: Paper Source PDF document 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. 4: Paper Source PDF document 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. 4: Paper Source PDF document 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. 4: Paper Source PDF document 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. 4: Paper Source PDF document Paper's Title: Inequalities for Functions of Selfadjoint Operators on Hilbert Spaces: a Survey of Recent Results Author(s): Sever S. Dragomir1,2 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. 4: Paper Source PDF document 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 {ek}k=1 is an orthonormal basis for H, then {Aek}k=1 is a 1-tight frame for H. 4: Paper Source PDF document 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. 4: Paper Source PDF document 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. 4: Paper Source PDF document Paper's Title: Rational Expressions of Arithmetic and Geometric Means for the Sequence npn ∈ 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 npn ∈ N and the geometric progression. We obtain the results associated with the rational expressions of the means. 4: Paper Source PDF document 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. 4: Paper Source PDF document 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. 4: 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. 4: 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. 4: Paper Source PDF document 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. 4: Paper Source PDF document 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 Frčres 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. 4: Paper Source PDF document Paper's Title: Boundness of the Power Exponential Function a2b +b2a 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 a2b +b2a for nonnegative real numbers a and b. The author proved that the function has the maximum value 1 for a + b = ˝, but it is no known that the minimum value for a + b = ˝. In this paper, we give the new proof of the function has the maximum value 1 and show that a2b +b2a > 0.989905 for a + b = ˝. 4: Paper Source PDF document 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 Ap 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. 4: Paper Source PDF document 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=QT+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. 3: Paper Source PDF document 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. 3: Paper Source PDF document 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. 3: Paper Source PDF document 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. 3: Paper Source PDF document 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 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. 3: Paper Source PDF document 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. 3: Paper Source PDF document 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. 3: Paper Source PDF document 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. 3: Paper Source PDF document 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). 3: Paper Source PDF document 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. 3: Paper Source PDF document 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 3: Paper Source PDF document 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. 3: Paper Source PDF document 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. 3: Paper Source PDF document 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. 3: 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. 3: Paper Source PDF document Paper's Title: Iterated Order of Fast Growth Solutions of Linear Differential Equations Author(s): Benharrat Belaďdi 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) + Ak-1 (z) f(k-1) +...+ A1 (z) f' + A0 (z) f= F (z), where Ao (z), ..., Ak-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 As is being dominant in the sense that it has larger growth than Aj (j≠s) and F. 3: Paper Source PDF document 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(Bl) 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. 3: 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. 3: Paper Source PDF document 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. 3: Paper Source PDF document 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=(xn), the difference sequence Δx is given by Δx=(Δxn) = (xn-xn-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. 3: Paper Source PDF document 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. 3: Paper Source PDF document Paper's Title: Ergodic Solenoidal Homology II: Density of Ergodic Solenoids Author(s): Vicente Muńoz and Ricardo Pérez Marco Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Serrano 113 bis, 28006 Madrid, Spain and Facultad de Matem áticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid, Spain CNRS, LAGA UMR 7539, Universit é 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. 3: Paper Source PDF document 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. 3: Paper Source PDF document 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. 3: Paper Source PDF document 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. 3: 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. 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. 3: Paper Source PDF document 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) |ak| ≤ nRn-1p∥, R → ∞. 3: Paper Source PDF document 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. 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. 3: 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. 3: Paper Source PDF document 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. 3: Paper Source PDF document 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. 3: Paper Source PDF document 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. 3: Paper Source PDF document 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. 3: Paper Source PDF document 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. 3: 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 Tf 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 Tf , 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. 3: Paper Source PDF document Paper's Title: Harmonic Functions with Positive Real Part Author(s): Sďbel 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. 3: Paper Source PDF document 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 KX. 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. 3: Paper Source PDF document 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. 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. 3: Paper Source PDF document 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. 3: 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 αi and βi are positive constants and pi(t) and qi(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. 3: Paper Source PDF document 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. 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. 3: 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 Rd and on the torus Td 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. 3: Paper Source PDF document 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. 3: Paper Source PDF document 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. 3: Paper Source PDF document 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. 3: Paper Source PDF document 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. 3: Paper Source PDF document Paper's Title: Characterization of Caristi Type Mapping Through its Absolute Derivative Author(s): M. Muslikh1, A. Kilicman2,3, 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. 3: Paper Source PDF document 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. 3: Paper Source PDF document 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. 3: Paper Source PDF document 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,...,xn are linearly independent in X and if y1,y2,...,yn are in X, then there exists an a A such that π(a)xi=yi 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. 3: 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. 3: Paper Source PDF document 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). 3: 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. 3: 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. 3: Paper Source PDF document 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, 3: Paper Source PDF document 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. 3: Paper Source PDF document 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. 3: Paper Source PDF document Paper's Title: Trace Inequalities for Operators in Hilbert Spaces: a Survey of Recent Results Author(s): Sever S. Dragomir1,2 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: https://rgmia.org/dragomir Abstract: In this paper we survey some recent trace inequalities for operators in Hilbert spaces that are connected to Schwarz's, Buzano's and Kato's inequalities and the reverses of Schwarz inequality known in the literature as Cassels' inequality and Shisha-Mond's inequality. Applications for some functionals that are naturally associated to some of these inequalities and for functions of operators defined by power series are given. Further, various trace inequalities for convex functions are presented including refinements of Jensen inequality and several reverses of Jensen's inequality. Hermite-Hadamard type inequalities and the trace version of Slater's inequality are given. Some Lipschitz type inequalities are also surveyed. Examples for fundamental functions such as the power, logarithmic, resolvent and exponential functions are provided as well. 3: Paper Source PDF document 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. 3: Paper Source PDF document 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. 3: Paper Source PDF document 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. 3: Paper Source PDF document 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 GPt,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. 3: Paper Source PDF document Paper's Title: Preserver of Local Spectrum of Skew-product Operators Author(s): Rohollah Parvinianzadeh1,*, 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 σT(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 σφ1(T)φ2(S)*(k0)= σTS*(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. 3: 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 3: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. URL : 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. 2: Paper Source PDF document 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 School of Mathematical Sciences, Faculty of Sciences and Technology, Ukm, Banki 43600, Malaysia Department of Mathematics, Islamiah College, V aniambadi 635 751, India Department of Mathematics, Madras Christian College, Tambaram, Chennai- 600 059, India 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document Paper's Title: On Perturbed Reflection Coefficients Author(s): J. L. Díaz-Barrero and J. J. Egozcue Applied Mathematics III, Universidad Politécnica de Cataluńa, 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 L˛-norm on the unit circle . The proof is constructive and can be used algorithmically. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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, Jan áčkovo 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. 2: Paper Source PDF document Paper's Title: Note on the Rank of Birkhoff Interpolation Author(s): J. Rubió-Massegú Applied Mathematics III, Universitat Politčcnica 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. 2: 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: 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 Săo Paulo, Caixa Postal 668, 13560-970, Săo 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. 2: Paper Source PDF document 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=qN 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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, Universitŕ 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 2: Paper Source PDF document 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). 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document Paper's Title: Equivalence of the Nonsmooth Nonlinear Complementarity Problems to Unconstrained Minimization Author(s): M. A. Tawhid and J. L. Goffin Department of Mathematics and Statistics, School of Advanced Technologies and Mathematics, Thompson Rivers University, 900 McGill Road, PO Box 3010, Kamloops, BC V2C 5N3 Canada Alexandria University and Egypt Japan University of Science and Technology, Alexandria-Egypt mtawhid@tru.ca Faculty of Management, McGill University, 1001 Sherbrooke Street West, Montreal, Quebec, H3A 1G5 Canada. Jean-Louis.Goffin@McGill.ca Abstract: This paper deals with nonsmooth nonlinear complementarity problem, where the underlying functions are nonsmooth which admit the H-differentiability but not necessarily locally Lipschitzian or directionally differentiable. We consider a reformulation of the nonlinear complementarity problem as an unconstrained minimization problem. We describe H-differentials of the associated penalized Fischer-Burmeister and Kanzow and Kleinmichel merit functions. We show how, under appropriate P0, semimonotone (E0), P, positive definite, and strictly semimonotone (E) -conditions on an H-differential of f, finding local/global minimum of a merit function (or a stationary point' of a merit function) leads to a solution of the given nonlinear complementarity problem. Our results not only give new results but also unify/extend various similar results proved for C1. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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 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). 2: Paper Source PDF document 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. 2: Paper Source PDF document 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 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. 2: Paper Source PDF document 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 a3b + b3a + ( (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. 2: Paper Source PDF document 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. 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document Paper's Title: Some Grüss Type Inequalities in Inner Product Spaces Author(s): Sever S. Dragomir1,2 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document Paper's Title: Robust Error Analysis of Solutions to Nonlinear Volterra Integral Equation in Lp 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. 2: Paper Source PDF document 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-mail1rashida12@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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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. 2: Paper Source PDF document 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,t21 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:

Invariant Subspaces Close to Almost Invariant Subspaces for Bounded Linear Operators

Author(s):

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.

Department of Mathematical and Statistical Sciences,
University of Birjand,
PO Box 97175/615, Birjand,
Iran.

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:

Polynomial Dichotomy of C0-Quasi Semigroups in Banach Spaces

Author(s):

Sutrima1,2, 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,
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.

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Paper's Title:

Numerical Radius Isometries between Hermitian Banach Algebras

Author(s):

Mohamed Mabrouk and Ashwaq Albideewi

Department of Mathematics,
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:

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:

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 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,
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:

Applications of Von Neumann Algebras to Rigidity Problems of (2-Step) Riemannian (Nil-)Manifolds

Author(s):

DFouman Faculty of Engineering,
College of Engineering, University of Tehran,
Iran.

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:

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,
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.

2: Paper Source PDF document

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.

2: Paper Source PDF document

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.

2: Paper Source PDF document

Paper's Title:

Hermite-Hadamard Type Inequalities for MN-Convex Functions

Author(s):

Sever S. Dragomir1,2

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.

2: Paper Source PDF document

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.

2: Paper Source PDF document

Paper's Title:

Coefficient Estimates Of Sakaguchi Kind Functions Using Lucas Polynomials

Author(s):

H. Priya and B. Srutha Keerthi

Department of Mathematics,
VIT Chennai Campus,
Chennai - 600 048,
India.
E-mail: priyaharikrishnan18@gmail.com

Department of Mathematics,
VIT Chennai Campus,
Chennai - 600 048,
India.
E-mail: i
sruthilaya06@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.

2: Paper Source PDF document

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.
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.

2: Paper Source PDF document

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.

2: Paper Source PDF document

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.

2: Paper Source PDF document

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.

2: Paper Source PDF document

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.

2: Paper Source PDF document

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.

2: Paper Source PDF document

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:

2: Paper Source PDF document

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.

2: Paper Source PDF document

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

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.

2: Paper Source PDF document

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.

2: Paper Source PDF document

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.

2: 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.

2: Paper Source PDF document

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.

2: Paper Source PDF document

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.

2: Paper Source PDF document

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.

2: 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.

2: Paper Source PDF document

Paper's Title:

On the Oscillatory Behavior of Self Adjoint Fractional Extensible Beam Equations

Author(s):

1Post Graduate and Research Department of Mathematics,
Thiruvalluvar Government Arts College,
Rasipuram - 637 401, Namakkal Dt., Tamil Nadu,
India.

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.

1: Paper Source PDF document

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

U
rl: 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.

1: Paper Source PDF document

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

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.

1: Paper Source PDF document

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
Url
: h
ttp://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,
M
alaysia
maslina@pkrisc.cc.ukm.my
Url
:

Department of Mathematics, Madras Christian College, Tambaram, Chennai 600 059, India

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

1: Paper Source PDF document

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

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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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,
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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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,
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.

1: Paper Source PDF document

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,
Str. Armatei Romane no.5,
Romania
smbica@yahoo.com

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.

1: Paper Source PDF document

Paper's Title:

Stability of a Pexiderized Equation

Author(s):

Maryam Amyar

Department of Mathematics,
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.

1: 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.

1: Paper Source PDF document

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

1: Paper Source PDF document

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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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,
shan@annauniv.edu

Department of Mathematics,
Valliammai Engineering College,
Chennai-603 203,
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.

1: Paper Source PDF document

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.

1: 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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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
jeyaraman-mp@yahoo.co.i

Department of Mathematics
Valliammai Engineering College
Chennai - 603203
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.

1: Paper Source PDF document

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
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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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,
mdjohnst@math.uwaterloo.ca

Department of Mathematics & Statistics, University of Guelph,
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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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.

1: 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 * ΩN by f1(x,ω) = f(x,ω1)  and fn+1(x,ω)=f(fn(x,ω),ωn+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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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),,
Iran

moslehian@ferdowsi.um.ac.ir
niknam@math.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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

Paper's Title:

Neighborhoods of Certain Subclasses of Analytic Functions of Complex Order with Negative Coefficients

Author(s):

Department of Applied Mathematics,
Sri Venkateswara College of Engineering,
Sriperumbudur, Chennai - 602105,
India.

Department of Mathematics,
Chennai - 600059,
India

Department of Applied Mathematics,
Sri Venkateswara College of Engineering,
Sriperumbudur, Chennai - 602105,
India.

Department of Mathematics,
Easwari Engineering College,
Ramapuram, Chennai - 600089,
India

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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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

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

1: Paper Source PDF document

Paper's Title:

Solution of One Conjecture on Inequalities with Power-Exponential Functions.

Author(s):

Seiichi Manyama

Osaka University

Japan

manchanr4@gmail.com

Abstract:

In this paper, we prove the open inequality aea+beb aeb+bea for all positive real numbers a and b.

1: Paper Source PDF document

Paper's Title:

SEVERAL q-INTEGRAL INEQUALITIES

Author(s):

W. T. Sulaiman

Department of Computer Engineering,
College of Engineering,
University of Mosul,
Iraq
.

Abstract:

In the present paper several q-integral inequalities are presented, some of them are new and others are generalizations of known results.

1: Paper Source PDF document

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 Lp 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

1: Paper Source PDF document

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.

1: Paper Source PDF document

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 Systčmes,
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 Systčmes,
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 Ak, Bk for all k∈{2,...,k}, are any positive semidefinite matrices.

1: Paper Source PDF document

Paper's Title:

Uniform Convergence of Schwarz Method for Noncoercive Variational Inequalities Simple Proof

Author(s):

Department of mathematics, LANOS Laboratory,
Faculty of the Sciences, University Badji Mokhtar,
P.O 23000 Annaba,
Algeria.

haiourm@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.

1: Paper Source PDF document

Paper's Title:

An Lp Inequality for Self-Reciprocal' Polynomials. II

Author(s):

M. A. Qazi

Department of Mathematics,
Tuskegee University,
Tuskegee, Alabama 36088
U.S.A.

Abstract:

The main result of this paper is a sharp integral mean inequality for the derivative of a `self-reciprocal' polynomial.

1: Paper Source PDF document

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

Piata Tineretului no. 8,
Romania

Str. Universitatii No. 1,
Romania

loredana.galea@univagora.ro
smbica@yahoo.com

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.

1: Paper Source PDF document

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,
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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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

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.

1: Paper Source PDF document

Paper's Title:

Schwarz Method for Variational Inequalities Related to Ergodic Control Problems

Author(s):

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. Boulbrachčne 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.

1: Paper Source PDF document

Paper's Title:

New Solutions to Non-Smooth PDEs

Author(s):

Moawia Alghalith

University of the West Indies,
St. Augustine,

moawia.alghalith@sta.uwi.edu

Abstract:

We provide strong solutions to partial differential equations when the function is non-differentiable.

1: Paper Source PDF document

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
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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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.

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.

1: Paper Source PDF document

Paper's Title:

Some interesting properties of finite continuous Cesŕro 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,
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 Lp([0,1]), where C1 is the Cesŕro operator defined on the complex Banach spaces Lp([0 , 1])  for 1<p<∞ by the expression

1: Paper Source PDF document

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 {Ti}i=1 be a family of J-nonexpansive maps, where, for each i,~Ti maps E to 2E*. 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 {Ti}i=1 is nonempty, an iterative scheme is constructed and proved to converge strongly to a point x* in n=1FJTi. 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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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,

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.

1: Paper Source PDF document

Paper's Title:

Integrating Factors and First Integrals of a Class of Third Order Differential Equations

Author(s):

Department of Mathematics,
Yarmouk University,
Irbid 21163,
Jordan.

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.

1: Paper Source PDF document

Paper's Title:

Author(s):

Department of Mathematics,
University of Msila 28000,
ALGERIA.
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.

1: Paper Source PDF document

Paper's Title:

Generalized k-distance-balanced Graphs

Author(s):

Amir Hosseini and Mehdi Alaeiyan

Department of mathematics, Karaj Branch,
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.

1: Paper Source PDF document

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,

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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

Paper's Title:

A New Interpretation of the Number e

Author(s):

Olivier de La Grandville

Faculty of Economics, Goethe University,
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.

1: Paper Source PDF document

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.]

1: 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,
Iraq.

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.

1: Paper Source PDF document

Paper's Title:

Simplicial (co)-homology of Band Semigroup

Author(s):

Yasser Farhat

Abu Dhabi Polytechnic,
P.O. Box 111499, Abu Dhabi,
UAE.

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 n1. This proceeds in three steps. In each step, we introduce a bounded linear map. By iteration in each step, we achieve our goal.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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, Prishtin
ë 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.

1: Paper Source PDF document

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.
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

1: 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

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

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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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), xR. In this paper we obtain a pointwise convergence theorem for the Fourier-type series with respect to the orthonormal polynomials {pn(w2;x)}.

1: Paper Source PDF document

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.

1: 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,
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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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.

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.

1: Paper Source PDF document

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 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+1Fq(z) for q= 2, 3, 4. This is achieved by means of separating the generalized hypergeometric function q+1Fq(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.

1: Paper Source PDF document

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 Fkn + r and the Lucas numbers Lkn + r are presented. Each is established using methods that rely on nothing beyond elementary integral calculus.

1: Paper Source PDF document

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.

1: Paper Source PDF document

Paper's Title:

Metric Functionals for the Hästö Metric

Author(s):

G. Bettencourt and S. Mendes

Departamento de Matemática,
Covilhă Portugal,
Centro de Matemática e Aplicaçőes
Covilhă Portugal.
E-mail: gastao@ubi.pt

ISCTE - University Institute of Lisbon - Lisbon Portugal,
Centro de Matemática e Aplicaçőes
Covilhă 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.

1: Paper Source PDF document

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,
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.

1: Paper Source PDF document

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,
VIT Chennai Campus, Chennai - 600 048,
India.
E-mail: priyaharikrishnan18@gmail.com, priya.h2020@vitstudent.ac.in

Department of Mathematics,
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.

1: Paper Source PDF document

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.

1: Paper Source PDF document

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.