


Paper's Title:
Error Bounds for Numerical Integration of Functions of Lower Smoothness and GaussLegendre 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.
Email: 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 GaussLegendre 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 GaussLegendre 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.
Paper's Title:
On Perturbed Reflection Coefficients
Author(s):
J. L. DíazBarrero and J. J. Egozcue
Applied Mathematics III,
Universidad Politécnica de Cataluña,
Barcelona, Spain
jose.luis.diaz@upc.edu
juan.jose.egozcue@upc.edu
Abstract:
Many control and signal processing applications require testing stability of polynomials. Classical tests for locating zeros of polynomials are recursive, but they must be stopped whenever the so called "singular polynomials" appear. These ``singular cases'' are often avoided by perturbing the "singular polynomial". Perturbation techniques although always successful are not proven to be wellfounded. 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 nonsingular polynomials are proven to be dense in the set of all polynomials respect the L²norm on the unit circle . The proof is constructive and can be used algorithmically.
Paper's Title:
Hardy Type Inequalities via Convexity  The Journey so Far
Author(s):
James A.
Oguntuase and LarsErik Persson
Department of Mathematics,
University of Agriculture,
P. M. B. 2240, Abeokuta, Nigeria.
Department of
Mathematics, Luleå University of Technology,
SE971 87, Luleå , Sweden.
oguntuase@yahoo.com,
larserik@sm.luth.se .
Abstract:
It is nowadays wellknown 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.
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.
Email: sharmavishal911@gmail.com
Department of Mathematics,
Central University of Jammu,
Jammu and Kashmir,
India.
Email: sanjaykmath@gmail.com
Department of Mathematics,
Central University of Jammu,
Jammu and Kashmir,
India.
Email: stanzin.math@cujammu.ac.in
Abstract:
In this paper, we characterize boundedness, compactness and find the essential norm estimates for generalized composition operators between Besov spaces and S_{p} spaces.
Paper's Title:
Viability
Theory And Differential Lanchester Type Models For Combat.
Differential Systems.
Author(s):
G. Isac and A. Gosselin
Department Of
Mathematics, Royal Military College Of Canada,
P.O. Box 17000, Stn Forces, Kingston,
Ontario, Canada K7k 7b4
isacg@rmc.ca
gosselina@rmc.ca
URL:
http://www.rmc.ca/academic/math_cs/isac/index_e.html
URL:
http://www.rmc.ca/academic/math_cs/gosselin/index_e.html
Abstract:
In 1914, F.W. Lanchester proposed several mathematical models based on differential equations to describe combat situations [34]. Since then, his work has been extensively modified to represent a variety of competitions including entire wars. Differential Lanchester type models have been studied from many angles by many authors in hundreds of papers and reports. Lanchester type models are used in the planning of optimal strategies, supply and tactics. In this paper, we will show how these models can be studied from a viability theory stand point. We will introduce the notion of winning cone and show that it is a viable cone for these models. In the last part of our paper we will use the viability theory of differential equations to study Lanchester type models from the optimal theory point of view.
Paper's Title:
Ostrowski Type Inequalities for Lebesgue Integral: a Survey of Recent Results
Author(s):
Sever S. Dragomir^{1,2}
^{1}Mathematics, School of Engineering
& Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
Email: sever.dragomir@vu.edu.au
^{2}DSTNRF 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 realvalued 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.
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, 446702, Korea.
ghkim@kangnam.ac.kr
Department of Computer and Information Security
Daejeon University, Daejeon 300716, 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
Paper's Title:
Expected Utility with Subjective Events
Author(s):
Jacob Gyntelberg and Frank Hansen
Bank for International Settlements,
Basel,
Switzerland
Tohoku University, Institute for International Education,
Sendai,
Japan
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.
Paper's Title:
On Oscillation of SecondOrder 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 secondorder 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), 234252] and Erbe [Canad. Math. Bull. 16 (1973), 4956.] for differential equations. When T=Z the results include and improve some oscillation criteria for difference equations. When T=hZ, h>0, T=q^{N} and T=N^{2}, 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.
Paper's Title:
Some New Generalizations of Jensen's Inequality with Related Results and Applications
Author(s):
Steven G. From
Department of Mathematics
University of Nebraska at Omaha
Omaha, Nebraska 681820243.
Email: 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 byproducts of this method, we shall obtain some new HermiteHadamard inequalities for functions which are 3convex or 3concave. The new method works to obtain bounds for the Jensen gap for nonconvex 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.
Paper's Title:
The Jacobson Density Theorem for NonCommutative Ordered Banach Algebras
Author(s):
Kelvin Muzundu
University of Zambia,
Deparment of Mathematics and Statistics,
P.O. Box 32379, Lusaka,
Zambia.
Email: kmzundu@gmail.com
Abstract:
The Jacobson density theorem for general noncommutative Banach algebras states as follows: Let π be a continuous, irreducible representation of a noncommutative Banach algebra A on a Banach space X. If x_{1},x_{2},...,x_{n} are linearly independent in X and if y_{1},y_{2},...,y_{n} are in X, then there exists an a∈ A such that π(a)x_{i}=y_{i} for i=1,2,...,n. By considering ordered Banach algebras A and ordered Banach spaces X, we shall establish an ordertheoretic version of the Jacobson density theorem.
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, AlQassim,
Saudi Arabia.
Email: iqbal@qec.edu.sa,
i.ahmad@qu.edu.sa
Zakir Husain Delhi College,
University of Delhi,
JLN Marg, New Delhi 110 002,
India.
Email: abdullahdu@qec.edu.sa
Department of Mathematics,
Aligarh Muslim University, Aligarh,
India.
Email: 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.
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
AlAin, 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.
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 multiparameter families of congruences (mod p) are found for integer sums of q^{th} powers of the trigonometric functions over various sets of equidistant arguments, where p is any prime factor of q. Those congruences provide sensitive tests for the accuracy of software for evaluating trigonometric functions to high precision.
Paper's Title:
Nontrivial Solutions of Singular Superlinear Threepoint 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 threepoint 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.
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 KwazuluNatal,
Private Bag X54001, Durban 4001,
South Africa.
Email: 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).
Paper's Title:
Positive Periodic TimeScale 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 higherdimensional equations. Two pairs of corresponding nabla equations are also provided in an analogous manner.
Paper's Title:
Comparison Results for Solutions of Time Scale Matrix Riccati Equations and Inequalities
Author(s):
R. Hilscher
Department of Mathematical Analysis, Faculty of Science,
Masaryk University, Janáčkovo nám. 2a,
CZ60200, 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.
Paper's Title:
Hyperbolic Models Arising in the Theory of Longitudinal Vibration of Elastic Bars
Author(s):
^{1}I. Fedotov, ^{1}J. Marais, ^{1,2}M. Shatalov and ^{1}H.M. Tenkam
^{1}Department 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.
^{2}Manufacturing 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
MindlinHerrmann case in terms of Green functions. Finally, deductions regarding
the accuracy of the models are made by comparison with the exact
PochhammerChree solution for an isotropic cylinder.
Paper's Title:
Inequalities for Discrete FDivergence Measures: A Survey of Recent Results
Author(s):
Sever S. Dragomir^{1,2}
^{1}Mathematics, School of Engineering
& Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
Email: sever.dragomir@vu.edu.au
^{2}DSTNRF 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 fdivergence 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 KullbackLeibler Distance, Hellinger Discrimination and Varation distance are provided. Approximations of the fdivergence 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.
Paper's Title:
Polyanalytic Functions on Subsets of Z[i]
Author(s):
Abtin Daghighi
Linköping University,
SE581 83,
Sweden.
Email: abtindaghighi@gmail.com
Abstract:
For positive integers q we consider the kernel of the powers L^{q} where L is one of three kinds of discrete analogues of the CauchyRiemann operator. The first two kinds are wellstudied, 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 pseudopowers. We propose such multiplications together with associated pseudopowers. We develop a prooftool in terms of certain sets of uniqueness.
Paper's Title:
Fractional class of analytic functions Defined Using qDifferential Operator
Author(s):
K . R. Karthikeyan, Musthafa Ibrahim and S. Srinivasan
Department of Mathematics and
Statistics,
Caledonian College of Engineering, Muscat,
Sultanate of Oman.
Email: kr_karthikeyan1979@yahoo.com
College of Engineering,
University of Buraimi, Al Buraimi,
Sultanate of Oman.
Email: musthafa.ibrahim@gmail.com
Department of Mathematics, Presidency
College (Autonomous),
Chennai600005, Tamilnadu,
India.
Abstract:
We define a qdifferential fractional operator, which generalizes Salagean and Ruscheweyh differential operators. We introduce and study a new class of analytic functions involving qdifferential 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.
Paper's Title:
A Comparison Between Two Different Stochastic Epidemic Models with Respect to the Entropy
Author(s):
Farzad Fatehi and Tayebe Waezizadeh
Department of Mathematics,
University of Sussex,
Brighton BN1 9QH,
UK.
Email: 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 7616914111,
Iran.
Email: waezizadeh@uk.ac.ir
URL:
http://academicstaff.uk.ac.ir/en/tavaezizadeh
Abstract:
In this paper at first a brief history of mathematical models is presented with the aim to clarify the reliability of stochastic models over deterministic models. Next, the necessary background about random variables and stochastic processes, especially Markov chains and the entropy are introduced. After that, entropy of SIR stochastic models is computed and it is proven that an epidemic will disappear after a long time. Entropy of a stochastic mathematical model determines the average uncertainty about the outcome of that random experiment. At the end, we introduce a chain binomial epidemic model and compute its entropy, which is then compared with the DTMC SIR epidemic model to show which one is nearer to reality.
Paper's Title:
Approximately Dual pApproximate Schauder Frames
Author(s):
K. Mahesh Krishna and P. Sam Johnson
StatMath 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.
Email: 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.
Paper's Title:
An Algorithm to Compute GaussianType 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@univpau.fr
URL: http://www.univpau.fr/~aguessab/
Abstract:
It is wellknown 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.
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,
IleIfe,
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.
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 767987328
USA.
Johnny_Henderson@baylor.edu
Laboratoire de Mathématiques, Université de Sidi Bel Abbés
BP 89, 22000 Sidi Bel Abbées,
Algérie.
ouahab@univsba.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 LeraySchauder. For the global existence and uniqueness we apply a recent Frigon and Granas nonlinear alternative of LeraySchauder type in Fréchet spaces.
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 μordering which is a new method for ordering closed intervals.
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 KiZerbo,
Burkina Faso.
Email:
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
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, 570749,
Republic of Korea.
General Education Institute,
Konkuk University,
Chungju 380701,
Republic of Korea.
Department of Mathematics, School of
Engineering,
Sir Padampat Singhania University,
Bhatewar, Udaipur, 313601, Rajasthan State,
India.
Department of Mathematics,
Vedant College of Engineering and Technology,
(Rajasthan Technical University),
Bundi323021, Rajasthan,
India.
Email: 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 _{3}F_{2} due to Watson, Dixon and Whipple. Several new and interesting integrals have also been obtained from our main findings.
Paper's Title:
Solving NonAutonomous Nonlinear Systems of Ordinary Differential Equations Using MultiStage Differential Transform Method
Author(s):
K. A. Ahmad, Z. Zainuddin, F. A. Abdullah
School of Mathematical Sciences
Universiti Sains Malaysia
11800 USM Penang
Malaysia.
Email: abumohmmadkh@hotmail.com
zarita@usm.my
farahaini@usm.my
Abstract:
Differential equations are basic tools to describe a wide variety of phenomena in nature such as, electrostatics, physics, chemistry, economics, etc. In this paper, a technique is developed to solve nonlinear and linear systems of ordinary differential equations based on the standard Differential Transform Method (DTM) and Multistage Differential Transform Method (MsDTM). Comparative numerical results that we are obtained by MsDTM and RungeKutta method are proposed. The numerical results showed that the MsDTM gives more accurate approximation as compared to the RungeKutta numerical method for the solutions of nonlinear and linear systems of ordinary differential equations
Paper's Title:
Inequalities Relating to the Gamma Function
Author(s):
ChaoPing Chen and Feng Qi
Department of Applied Mathematics and Informatics,
Research Institute of Applied Mathematics,
Henan Polytechnic University, Jiaozuo
City, Henan 454000, China
chenchaoping@hpu.edu.cn
Department of Applied Mathematics and Informatics,
Research Institute of Applied Mathematics,
Henan Polytechnic University, Jiaozuo
City, Henan 454000, China
qifeng@hpu.edu.cn,
fengqi618@member.ams.org
Url:
http://rgmia.vu.edu.au/qi.html,
http://dami.hpu.edu.cn/qifeng.html
Abstract:
For _{}, we have
_{ }.
For_{},
_{ },
And equality occurs for x=1.
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 noncommutative extension of classical Itô stochastic calculus, known as quantum stochastic calculus, to the quantum BlackScholes 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.
Paper's Title:
Positive Solutions for Systems of Threepoint Nonlinear Boundary Value Problems
Author(s):
J. Henderson and S. K. Ntouyas
Department of Mathematics, Baylor University
Waco, Texas
767987328 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 threepoint 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 GuoKrasnosel'skii fixed point theorem is applied.
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 880038001,
USA.
mmariani@nmsu.edu
Abstract:
Longtime correlations in agricultural indices are studied and their behavior is compared to the wellestablished S&P500 index. Hurst exponent and Detrended Fluctuation Analysis (DFA) techniques are used in this analysis. We detected longcorrelations in the agricultural indices and briefly discussed some features specific in comparison to the S&P500 index.
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.
Email: 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, R_{0}, 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 R_{0} and that a quarantine success rate of at least 70% is sufficient to contain the disease outbreak.
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.
Email: 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
highorder 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 nuple integrals, while a
traditional approach would require  in some cases repeatedly  an
extension of Green's theorem to nspace.
Our paper is dedicated to the memory of Robert Dorfman (1916  2002).
Paper's Title:
Attempts to Define a BaumConnes Map Via Localization of Categories for Inverse Semigroups
Author(s):
Bernhard Burgstaller
Departamento de Matematica,
Universidade Federal de Santa Catarina,
CEP 88.040900 FlorianopolisSC,
Brasil.
Email:
bernhardburgstaller@yahoo.de
URL:
http://mathematik.work/bernhardburgstaller/index.html
Abstract:
An induction functor in inverse semigroup equivariant KKtheory 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 socalled Econtinuous inverse semigroup its equivariant KKtheory satisfies the universal property and is a triangulated category.
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
Email: hbolledla@gmail.com
Department of Mathematics,
Kakatiya Institute of Technology and Science
Email: dr.mh@kitsw.ac.in
Department of Mathematics,
Kakatiya University
Email: ladalla@gmail.com
Department of Mathematics,
Kakatiya University
Email: mperati@yahoo.com
Abstract:
To find the steady state probability vector of homogenous linear system π Q=0 of stochastic rate matrix Q, generalized triangular and symmetric (GTS) splitting method is presented. Convergence analysis and choice of parameters are given when the regularized matrix A=Q^{T}+ε I of the regularized linear system Ax=b is positive definite. Analysis shows that the iterative solution of GTS method converges unconditionally to the unique solution of the regularized linear system. From the numerical results, it is clear that the solution of proposed method converges rapidly when compared to the existing methods.
Paper's Title:
Existence of Nonspurious 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/mathaen.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 secondorder difference equations and twopoint 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 stepsize and thus there are no ``spurious'' solutions. It is shown that solutions of the discrete BVP will converge to solutions of ordinary differential equations.
Paper's Title:
Some Remarks on a Result of Bougoffa
Author(s):
James A. Oguntuase, LarsErik Persson and Josip E. Pečarič
Department of
Mathematics,University of Agriculture,
P M B 2240, Abeokuta, Nigeria
Department of Mathematics,
Luleå University of Technology,
SE971 87, Luleå , Sweden
Faculty of Textile Technology, University of Zagreb,
Pierottijeva 6, 10000 Zagreb, Croatia
oguntuase@yahoo.com,
larserik@sm.luth.se,
pecaric@hazu.hr.
Abstract:
Some new generalizations of the result of
L. Bougoffa [J. Inequal. Pure Appl. Math. 7 (2) (2006), Art. 60]
are derived and discussed.
Paper's Title:
On Generalization of Hardytype Inequalities
Author(s):
K. Rauf, S. Ponnusamy and J. O. Omolehin
Department of Mathematics,
University of Ilorin, Ilorin,
Nigeria
krauf@unilorin.edu.ng
Department of Mathematics,
Indian Institute of Technology Madras,
Chennai 600 036,
India
samy@iitm.ac.in
Department of Mathematics,
University of Ilorin, Ilorin,
Nigeria
omolehin_joseph@yahoo.com
Abstract:
This paper is devoted to some new generalization of Hardytype integral inequalities and the reversed forms. The study is to determine conditions on which the generalized inequalities hold using some known hypothesis. Improvement of some inequalities are also presented.
Paper's Title:
A OneLine 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 secondorder nonlinear 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).
Paper's Title:
New Inequalities of Mill's Ratio and Application to The Inverse Qfunction Approximation
Author(s):
Pingyi Fan
Department of Electronic Engineering,
Tsinghua University, Beijing,
China
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 Qfunction 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 Qfunction.
Paper's Title:
Evaluation of a New Class of Double Integrals Involving Generalized Hypergeometric Function _{4}F_{3}
Author(s):
Joohyung Kim, Insuk Kim and Harsh V. Harsh
Department of Mathematics Education,
Wonkwang University, Iksan, 570749,
Korea.
Email: joohyung@wku.ac.kr
Department of Mathematics Education,
Wonkwang University, Iksan, 570749,
Korea.
Email: iki@wku.ac.kr
Department of Mathematics, Amity School
of Eng. and Tech.,
Amity University Rajasthan
NH11C, Jaipur303002, Rajasthan,
India.
Email: harshvardhanharsh@gmail.com
Abstract:
Very recently, Kim evaluated some double integrals involving a generalized hypergeometric function _{3}F_{2} with the help of generalization of Edwards's wellknown 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 _{4}F_{3} 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.
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.
Paper's Title:
The RiemannStieltjes Integral on Time Scales
Author(s):
D. Mozyrska, E. Pawłuszewicz, D. Torres
Faculty Of Computer Science,
Białystok University Of Technology,
15351 Białystok,
Poland
d.mozyrska@pb.edu.pl
Department Of Mathematics,
University Of Aveiro,
3810193 Aveiro,
Portugal
ewa@ua.pt
Department Of Mathematics,
University Of Aveiro,
3810193 Aveiro,
Portugal
delfim@ua.pt
Abstract:
We study the process of integration on time scales in the sense of RiemannStieltjes. Analogues of the classical properties are proved for a generic time scale, and examples are given
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, 16851704. A stochastic extension of this model is proposed and discussed. Computer simulations suggest that the dynamics of the stochastic model includes a mixture of the dynamics observed in the deterministic model.
Paper's Title:
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 KrylovLanczos 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 2periodic extension of the interpolated function is smooth, the Eckhoff interpolation converges faster compared with the KrylovLanczos interpolation. This accelerated convergence is known as the autocorrection phenomenon. The paper presents a theoretical explanation of this phenomenon. Numerical experiments confirm theoretical estimates.
Paper's Title:
Hankel Operators on Copson's Spaces
Author(s):
Nicolae Popa
Institute of Mathematics of Romanian Academy,
P.O. BOX 1764
RO014700 Bucharest,
Romania.
Email: Nicolae.Popa@imar.ro, npopafoc@gmail.com
Abstract:
We give a characterization of boundedness of a Hankel matrix, generated by a pozitive decreasing sequence, acting on Copson's space cop(2).
Paper's Title:
A Low Order LeastSquares 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.
Email:
5772@zut.edu.cn
School of Mathematics and Statistics,
Zhengzhou University,
Zhengzhou 450001,
China.
Email:
shi_dy@126.com
Mathematics Department,
University of Southern Mississippi,
Hattiesburg MS, 39406,
U.S.A
Email:
huiqing.zhu@usm.edu
Abstract:
A low order leastsquares nonconforming finite element (NFE) method is proposed for magnetohydrodynamic equations with EQ_{1}^{rot} element and zeroorder RaviartThomas 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.
Paper's Title:
Countable Ordinal Spaces and Compact Countable Subsets of a Metric Space
Author(s):
B. AlvarezSamaniego, A. Merino
Nucleo de Investigadores Cientificos
Facultad de Ciencias,
Universidad Central del Ecuador (UCE)
Quito,
Ecuador.
Email: borys_yamil@yahoo.com,
balvarez@uce.edu.ec
Escuela de Ciencias Fisicas y Matematica
Facultad de Ciencias Exactas y Naturales
Pontificia Universidad Catolica del Ecuador
Apartado: 17012184, Quito,
Ecuador.
Email: 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 finitedimensional 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 alephone. We also show that for all cardinal number smaller than or equal to alephone, there exists a metric space with cardinality equals the aforementioned cardinal number.
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 Yatsen University,
Guangzhou, 510275,
P. R. China.
Email: xiehy33@mail2.sysu.edu.cn
Department of Mathematics,
Sun Yatsen University,
Guangzhou, 510275,
P. R. China.
Email: liuq325@mail2.sysu.edu.cn
Department of Mathematics,
Sun Yatsen University,
Guangzhou, 510275,
P. R. China.
Email: stslyj@mail.sysu.edu.cn
Abstract:
In this paper, we introduce new geometric constant C(X,a_{i},b_{i},c_{i},2) to measure the difference between isosceles orthogonality and special Carlsson orthogonalities. At the same time, we also present the geometric constant C(X,a_{i},b_{i},c_{i}), which is a generalization of the rectangular constant proposed by Joly. According to the inequality on isosceles orthogonality, we give the boundary characterization of these geometric constants. Then the relationship between these geometric constants and uniformly nonsquare property can also be discussed. Furthermore, we show that there is a close relationship between these geometric constants and some important geometric constants.
Paper's Title:
High Order Collocation Method for the Generalized KuramotoSivashinsky Equation
Author(s):
Zanele Mkhize, Nabendra Parumasur and Pravin Singh
School of Mathematics, Statistics and
Computer Sciences,
University of KwaZuluNatal,
Private Bag X 54001,
Durban 4000.
Email: 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 KuramotoSivashinsky equation. Various numerical simulations are presented to justify the computational efficiency of the proposed method.
Paper's Title:
Refinement Inequalities Among Symmetric Divergence Measures
Author(s):
Inder Jeet Taneja
Departamento de Matemática,
Universidade Federal de Santa Catarina, 88.040900
Florianópolis, Sc, Brazil
taneja@mtm.ufsc.br
URL: http://www.mtm.ufsc.br/~taneja
Abstract:
There are three classical divergence measures in the literature on information theory and statistics, namely, JeffryesKullbackLeiber’s Jdivergence, SibsonBurbeaRao’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 χ^{2}−divergence, and triangular discrimination are not based on logarithmic expressions. These six divergence measures are symmetric with respect to probability distributions. In this paper some interesting inequalities among these symmetric divergence measures are studied. Refinements of these inequalities are also given. Some inequalities due to Dragomir et al. [6] are also improved.
Paper's Title:
Numerical Studies on Dynamical Systems Method for Solving Illposed 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 illposed 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.
Paper's Title:
The Iterated Variational Method for the Eigenelements of a Class of TwoPoint Boundary Value Problems
Author(s):
Muhammed I. Syam and Qasem M. AlMdallal
Department of Mathematical Sciences, College of Science, UAE University,
P. O. Box 17551, AlAin,
United Arab Emirates
Q.Almdallal@uaeu.ac.ae
M.Syam@uaeu.ac.ae
Abstract:
The iterated variational method is considered in the approximation of eigenvalues and eigenfunctions for a class of two point boundary value problems. The implementation of this method is easy and competes well with other methods. Numerical examples are presented to show the efficiency of the method proposed. Comparison with the work of others is also illustrated.
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.
Abstract:
The purpose of this note is to demonstrate a new property of the general mean of order p of m ordered positive numbers . If p < 0 and if , the elasticity of with respect to x_{m}, defined by , tends towards zero, and therefore . This property is then applied to optimal growth theory.
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,
Cochin21, Kerala,
India.
Dept. of Mathematics, College of
Engineering,
Cherthala, Kerala,
India.
Abstract:
This paper deals with Szegö type limits for multiplication operators on L^{2} (R) with respect to Haar orthonormal basis. Similar studies have been carried out by Morrison for multiplication operators T_{f} using Walsh System and Legendre polynomials [14]. Unlike the Walsh and Fourier basis functions, the Haar basis functions are local in nature. It is observed that Szegö type limit exist for a class of multiplication operators T_{f} , f∈ L^{∞} (R) with respect to Haar (wavelet) system with appropriate ordering. More general classes of orderings of Haar system are identified for which the Szegö type limit exist for certain classes of multiplication operators. Some illustrative examples are also provided.
Paper's Title:
Positive Solutions to a System of Boundary Value Problems for HigherDimensional Dynamic Equations on Time Scales
Author(s):
I. Y. Karaca
Department of Mathematics,
Ege University,
35100 Bornova, Izmir,
Turkey
URL:
http://ege.edu.tr
Abstract:
In this paper, we consider the system of boundary value problems for higherdimensional 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.
Paper's Title:
Some Properties of the MarshallOlkin and Generalized CuadrasAugé 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
Email: Pranesh.Kumar@unbc.ca
Abstract:
We investigate some properties of the families of two parameter MarshallOlkin and Generalized CuadrasAugé copulas. Some new results are proved for copula parameters, dependence measure and mutual information. A numerical application is discussed.
Paper's Title:
Some Convergence Results for JungckAm Iterative Process In Hyperbolic Spaces
Author(s):
Akindele Adebayo Mebawondu and Oluwatosin Temitope Mewomo
School of Mathematics, Statistics and Computer Science,
University of KwaZuluNatal, Durban,
South Africa.
Email:
216028272@stu.ukzn.ac.za,
mewomoo@ukzn.ac.za
Abstract:
In this paper, we introduce a new three steps iterative process called JungckAM iterative process and show that the proposed iterative process can be used to approximate fixed points of Jungckcontractive type mappings and JungckSuzuki type mappings. In addition, we establish some strong and Δconvergence results for the approximation of fixed points of JungckSuzuki 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 JungckNoor, JungckSP, JungckCR and some existing iterative processes in the literature. Finally, stability, data dependency results for JungckAM iterative process is established and we present an analytical proof and numerical examples to validate our claim.
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.
Email:
margaritabustosgonzalez@uiowa.edu
The Ohio State University at Marion,
Department of Mathematics,
1465 Mount Vernon Avenue,
Marion, Ohio,
USA.
Email: 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 FermatTorricelli point of a triangle.
Paper's Title:
Coexisting Attractors and Bubbling Route to Chaos in Modified Coupled Duffing Oscillators
Author(s):
B. Deruni^{1}, A. S. Hacinliyan^{1,2}, E. Kandiran^{3}, A. C. Keles^{2}, S. Kaouache^{4}, M.S. Abdelouahab^{4}, N.E. Hamri^{4}
^{1}Department
of Physics,
University of Yeditepe,
Turkey.
^{2}Department
of Information Systems and Technologies,
University of Yeditepe,
Turkey
^{3}Department
of Software Development,
University of Yeditepe,
Turkey.
^{4}Laboratory
of Mathematics and their interactions,
University Center of Abdelhafid Boussouf,
Mila 43000,
Algeria.
Email:
berc890@gmail.com
ahacinliyan@yeditepe.edu.tr
engin.kandiran@yeditepe.edu.tr
cihan.keles@yeditepe.edu.tr
s.kaouache@centrunivmila.dz
medsalah3@yahoo.fr
n.hamri@centreunivmila.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.
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.
Email: 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.
Paper's Title:
Existence, Global Regularity and Uniqueness of Solutions of the NavierStokes 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 NavierStokes equations in are given for when the initial velocity for all integers q ≥ 0 and div u_{0 }= 0.
Paper's Title:
Additive Mappings on Semiprime Rings Functioning as Centralizers
Author(s):
Abu Zaid Ansari and Faiza Shujat
Department of Mathematics,
Faculty of Science,
Islamic University of Madinah, Madinah
K.S.A.
Email: ansari.abuzaid@gmail.com,
ansari.abuzaid@iu.edu.sa
Department of Mathematics,
Faculty of Science,
Taibah University, Madinah,
K.S.A.
Email: 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.
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.
Email: sivagamisundari.2298@gmail.com
Divison of Mathematics, School of
Advanced Sciences,
Vellore Institute of Technology, Chennai Campus, Chennai  600 127,
India.
Email: 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.
Paper's Title:
On the Oscillatory Behavior of Self Adjoint Fractional Extensible Beam Equations
Author(s):
S. Priyadharshini^{1}, G.E. Chatzarakis^{2}, S. L. Panetsos^{2} and V. Sadhasivam^{1}
^{1}Post
Graduate and Research Department of Mathematics,
Thiruvalluvar Government Arts College,
Rasipuram  637 401, Namakkal Dt., Tamil Nadu,
India.
Email: s.priya25april@gmail.com,
ovsadha@gmail.com
^{2}Department
of Electrical and Electronic Engineering Educators,
School of Pedagogical and Technological Education(ASPETE),
Marousi 15122, Athens,
Greece.
Email: 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.
Paper's Title:
On Stan Ulam and his Mathematics
Author(s):
Krzysztof Ciesielski and Themistocles M. Rassias
Mathematics Institute, Jagiellonian University,
Łjasiewicza 6,
30348 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.
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 SaintEtienne,
CIS  LPMG, UMR CNRS 5148, 158 cours Fauriel,
42023 SaintEtienne Cedex 2, France.
rivollier@emse.fr;
debayle@emse.fr; pinoli@emse.fr
Abstract:
Shape diagrams are representations in the Euclidean plane introduced to study 3dimensional and 2dimensional 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 thirtyone 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 thirtyone 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.
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 SaintEtienne,
CIS  LPMG, UMR CNRS 5148, 158 cours Fauriel,
42023 SaintEtienne Cedex 2, France.
rivollier@emse.fr;
debayle@emse.fr; pinoli@emse.fr
Abstract:
Shape diagrams are representations in the Euclidean plane introduced to study 3dimensional and 2dimensional 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 twentytwo 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 twentytwo 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.
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 SaintEtienne,
CIS  LPMG, UMR CNRS
5148,
158 cours Fauriel,
42023 SaintEtienne Cedex 2, France.
rivollier@emse.fr;
debayle@emse.fr; pinoli@emse.fr
Abstract:
Shape diagrams are representations in the Euclidean plane introduced to study 3dimensional and 2dimensional 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 twentytwo 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 twentytwo 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..
Paper's Title:
Subordination Results Associated with Hadamard Product
Author(s):
S. Sivasubramanian, C. Ramachandran and B. A. Frasin
Department of Mathematics,
University College of Engineering,
Anna University,
Saram604 307,
India
Department of Mathematics,
University College of Engineering,
Anna University,
Villupuram,
India
Department of Mathematics,
Al alBayt University,
P.O. Box: 130095 Mafraq,
Jordan
Abstract:
In the present investigation, we consider an unified class of functions of complex order using Hadamard's convolution. We obtain a necessary and sufficient condition for functions to be in these classes.
Paper's Title:
Existence Results for Second Order Impulsive Functional Differential Equations with Infinite Delay
Author(s):
M. Lakrib, A. Oumansour and K. Yadi
Laboratoire de Mathématiques, Université Djillali
Liabées, B.P. 89 Sidi Bel Abbès 22000, Algérie
mlakrib@univsba.dz
oumansour@univsba.dz
Laboratoire de Mathématiques, Université Abou Bekr
Belkaid, B.P. 119 Tlemcen 13000, Algérie
k_yadi@mail.univtlemcen.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.
Paper's Title:
On the Boundedness of Hardy's Averaging Operators
Author(s):
DahChin Luor
Department of Applied Mathematics,
IShou 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 ErdélyiKober operators.
Paper's Title:
EndPoint 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.
Email: ola@stanford.edu
Abstract:
We offer an intuitive explanation of the endpoint 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.
Paper's Title:
C*valued metric projection and MoorePenrose 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 35195363, Semnan,
Iran.
Center of Excellence in Nonlinear Analysis and Applications (CENAA),
Semnan University,
Iran.
Email: Madjid.Eshaghi@gmail.com
Department of Mathematics,
Shahid Beheshti University, Tehran,
Iran.
Email: Hedayat.fathi@yahoo.com
Department of Mathematical Sciences,
University of Arkansas, Fayetteville, Arkansas 72701,
USA.
Email: shossein@uark.net
Abstract:
Let t be a regular operator between Hilbert C^{*}modules and t^{†} be its MoorePenrose inverse. We give some characterizations for t^{†} based on C^{*}valued metric projection. MoorePenrose inverse of bounded operators and elements of a C^{*}algebra is studied as a special case.
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 193953697, Tehran,
Iran.
.Email:
maryam_nikbakht@pnu.ac.ir
Department of Mathematics,
Faculty of Basic Science,
Shiraz University of Technology.
Email:
a_fakharzadeh@sutech.ac.ir
Department of Mathematics,
Payame Noor University,
P.O.Box 193953697, Tehran,
Iran.
Email: aheidari@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.
Paper's Title:
Convergence Speed of Some Random ImplicitKirktype Iterations for Contractivetype 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.
Email: 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 implicitKirk multistep iterative scheme and prove strong convergence and stability results for a class of generalized contractivetype 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.
Paper's Title:
The Concept of Convergence for 2Dimensional 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.
Email: 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 2dimensional 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 2dimensional subspaces of inner product spaces.
Paper's Title:
Bounds on the Jensen Gap, and Implications for MeanConcentrated 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.
Email: 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.
Paper's Title:
Applications of Von Neumann Algebras to Rigidity Problems of (2Step) Riemannian (Nil)Manifolds
Author(s):
Atefeh HasanZadeh and HamidReza Fanai
DFouman Faculty of Engineering,
College of Engineering, University of Tehran,
Iran.
Email: hasanzadeh.a@ut.ac.ir
Department of Mathematical Sciences,
Sharif University of Technology,
Iran
Email: 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 2step nilmanifolds.
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.
Email: joneytun123@gmail.com
Abstract:
In this paper we characterize the compactness of double difference of three noncompact composition operators on Bloch space induced by three holomorphic self maps on the unit disc.
Paper's Title:
Existence and Approximation of Traveling Wavefronts for the Diffusive MackeyGlass Equation
Author(s):
C. RamirezCarrasco and J. MolinaGaray
Facultad de Ciencias Basicas,
Universidad Catolica del Maule, Talca,
Chile
Email: carloshrc1989@gmail.com
molina@imca.edu.pe
Abstract:
In this paper, we consider the diffusive MackeyGlass 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 upperlower solutions. Finally, through an iterative procedure, we show numerical simulations that approximate the traveling wavefronts, thus confirming our theoretical results.
Paper's Title:
A Review on Minimally Supported Frequency Wavelets
Author(s):
K Pallavi^{1}, M C Lineesh^{1}, A Noufal^{2}
^{1}Department of
Mathematics,
National Institute of Technology Calicut,
Kerala 673601,
India.
Email:
pavikrishnakumar@gmail.com
lineesh@nitc.ac.in
^{2}Department of Mathematics,
Cochin University of Science and Technology,
Kerala 682022,
India.
Email: 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 lowpass 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, selementary wavelets and unimodular wavelets are also considered due to the similarity in definitions. Examples and illustrations are provided for more clarity.
Paper's Title:
Trace Inequalities for Operators in Hilbert Spaces: a Survey of Recent Results
Author(s):
Sever S. Dragomir^{1,2}
^{1}Mathematics,
School of Engineering
& Science
Victoria University,
PO Box 14428
Melbourne City, MC 8001,
Australia
Email: sever.dragomir@vu.edu.au
^{2}DSTNRF 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 ShishaMond'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. HermiteHadamard 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.
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.
Email:
dickson@periyaruniversity.ac.in,
padmasekarans@periyaruniversity.ac.in
Electrical and Electronic Engineering
Educators, School of
Pedagogical and Technological Education (ASPETE),
Marousi 15122, Athens,
Greece.
Email: 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 COVID19 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.
Paper's Title:
A Self Adaptive Method for Solving Split Bilevel Variational Inequalities Problem in Hilbert Spaces
Author(s):
Francis Akutsah^{1}, Ojen Kumar Narain^{2}, Funmilayo Abibat Kasali^{3} Olawale Kazeem Oyewole^{4} and Akindele Adebayo Mebawondu^{5}
^{1}School
of Mathematics,
Statistics and Computer Science,
University of KwaZuluNatal, Durban,
South Africa.
Email: 216040405@stu.ukzn.ac.za,
akutsah@gmail.com
^{2}School
of Mathematics,
Statistics and Computer Science,
University of KwaZuluNatal, Durban,
South Africa.
Email: naraino@ukzn.ac.za
^{3}Mountain Top University,
Prayer City, Ogun State,
Nigeria.
Email: fkasali@mtu.edu.ng
^{4}TechnionIsrael
Institute of Technology.
Email: 217079141@stu.ukzn.ac.za,
oyewoleolawalekazeem@gmail.co
^{5}School
of Mathematics,
Statistics and Computer Science,
University of KwaZuluNatal, Durban,
South Africa.
DSTNRF Centre of Excellence in Mathematical and Statistical Sciences (CoEMaSS),
Johannesburg,
South Africa.
Mountain Top University,
Prayer City, Ogun State,
Nigeria.
Email: 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 αstrongly 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.
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.
Paper's Title:
New Proofs of the Grüss Inequality
Author(s):
A.Mc.D. Mercer and Peter R. Mercer
Dept. Mathematics and Statistics,
University of Guelph, Guelph, Ontario,
Canada.
amercer@reach.net
Dept. Mathematics,
S.U.N.Y. College at Buffalo, Buffalo, NY,
U.S.A.
mercerpr@math.buffalostate.edu
Abstract:
We present new proofs of the Grüss inequality in its original form and in its linear functional form.
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 _{}
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 wellknown oscillation conditions _{} and _{} are not satisfied. The results obtained essentially improve known results in the literature.
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,
PhaseIII, 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.
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, Bangalore560 090,
INDIA.
vasuki_kr@hotmail.com
Abstract:
In this paper, we give new proof of certain RamanujanSchläfli modular equations. We also obtain a new modular equation of degree 23.
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.
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 piecewisesmooth 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.
Paper's Title:
Existence of Large Solutions to NonMonotone 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
WrightPatterson Air Force Base, OH, 454337765,
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.
Paper's Title:
Error Inequalities for Weighted Integration Formulae and Applications
Author(s):
Nenad Ujević and Ivan Lekić
Department of Mathematics
University of Split
Teslina 12/III, 21000 Split
CROATIA.
ujevic@pmfst.hr
ivalek@pmfst.hr
Abstract:
Weighted integration formulae are derived. Error inequalities for the weighted integration formulae are obtained. Applications to some special functions are also given.
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.
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).
Paper's Title:
Topological Aspects of Scalarization in Vector Optimization Problems.
Author(s):
Peter I. Kogut, Rosanna Manzo and Igor V. Nechay
Department of Differential Equations,
Dnipropetrovsk National University, Naukova
STR.,
13,
49010 Dnipropetrovsk,
Ukraine
p.kogut@i.ua
Università di Salerno,
Dipartimento di Ingegneria dell'Informazione e Matematica Applicata,
Via Ponte don Melillo, 84084 Fisciano (SA),
Italy
manzo@diima.unisa.it
Department of Technical Cybernetics,
Dnipropetrovsk Technical University,
Acad. Lazarjan
STR., 2,
49010 Dnipropetrovsk,
Ukraine
i.nechay@i.ua
Abstract:
In this paper, we study vector optimization problems in partially ordered Banach spaces. We suppose that the objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. We derive sufficient conditions for existence of efficient solutions of the above problems and discuss the role of topological properties of the objective space. We discuss the scalarization of vector optimization problems when the objective functions are vectorvalued mappings with a weakened property of lower semicontinuity. We also prove the existence of the socalled generalized efficient solutions via the scalarization process. All principal notions and assertions are illustrated by numerous examples.
Paper's Title:
SEVERAL qINTEGRAL INEQUALITIES
Author(s):
W. T. Sulaiman
Department of Computer Engineering,
College of Engineering,
University of Mosul,
Iraq.
waadsulaiman@hotmail.com
Abstract:
In the present paper several qintegral inequalities are presented, some of them are new and others are generalizations of known results.
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,
AlexandriaEgypt
mtawhid@tru.ca
Faculty of Management, McGill University,
1001 Sherbrooke Street West, Montreal, Quebec, H3A 1G5
Canada.
JeanLouis.Goffin@McGill.ca
Abstract:
This paper deals with nonsmooth nonlinear complementarity problem, where the underlying functions are nonsmooth which admit the Hdifferentiability but not necessarily locally Lipschitzian or directionally differentiable. We consider a reformulation of the nonlinear complementarity problem as an unconstrained minimization problem. We describe Hdifferentials of the associated penalized FischerBurmeister and Kanzow and Kleinmichel merit functions. We show how, under appropriate P_{0}, semimonotone (E_{0}), P, positive definite, and strictly semimonotone (E) conditions on an Hdifferential 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 C^{1}.
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, Mysore570 006
India
dsomashekara@yahoo.com
Department of Mathematics,
The National Institute of Engineering,
Mysore570 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 qgamma, qbeta and etafunction identities from the three variable reciprocity theorem.
Paper's Title:
On A Conjecture of A Logarithmically Completely Monotonic Function
Author(s):
Valmir Krasniqi, Armend Sh. Shabani
Department of Mathematics,
University of Prishtina,
Republic of Kosova
Email:
vali.99@hotmail.com
armend_shabani@hotmail.com
Abstract:
In this short note we prove a conjecture, related to a logarithmically completely monotonic function, presented in [5]. Then, we extend by proving a more generalized theorem. At the end we pose an open problem on a logarithmically completely monotonic function involving qDigamma function.
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.
Email: 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.
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, 7591474831,
Iran.
Email: 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.
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.
Email:
andreasboukas@yahoo.com
Email: pfeinsil@math.siu.edu
Abstract:
Using Bartle's bilinear vector integral we define stochastic integrals of bounded operator valued functions with respect to Stieltjes measures associated with the generators of the Heisenberg and Finite Difference Lie algebras. Our definition also covers the Square of White Noise and sl/2 Lie algebras.
Paper's Title:
On The RayleighLove Rod Accreting In Both Length And CrossSectional Area: Forced And Damped Vibrations
Author(s):
M.L.G. Lekalakala^{1}, M. Shatalov^{2}, I. Fedotov^{3}, S.V. Joubert^{4}
^{1}Department
of Mathematics, Vaal University of Technology, P.O. Box 1889, Secunda, 2302,
South Africa.
Email^{1}:
glen@vut.ac.za
^{2,3,4}Department 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 KelvinVoigt. 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 crosssectional area as it vibrates. The problem arising and the dynamics of the vibrating rod are described and investigated within the RayleighLove 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 GalerkinKantorovich 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.
Paper's Title:
New Implicit KirkType Schemes for General Class of QuasiContractive Operators in Generalized Convex Metric Spaces
Author(s):
K. Rauf, O. T. Wahab and A. Ali
Department of Mathematics,
University of Ilorin, Ilorin,
Nigeria.
Email: 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 Kirktype iterative schemes in generalized convex metric spaces in order to approximate fixed points for general class of quasicontractive type operators. The strong convergence, Tstability, 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.
Paper's Title:
Inequalities for Functions of Selfadjoint Operators on Hilbert Spaces:
a Survey of Recent Results
Author(s):
Sever S. Dragomir^{1,2}
^{1}Mathematics,
College of Engineering
& Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
Email: sever.dragomir@vu.edu.au
^{2}DSTNRF 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.
Paper's Title:
Analysis of the Dynamic Response of the Soilpile 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.
Email: imbaye@univthies.sn
mamadou.diop@univthies.sn
aliousonko59@gmail.com
mmalickba@hotmail.fr
URL: https://www.univthies.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 LaxMilgram theorem and the spectral theory thus the existence of a Hilbert basis is shown and the spectral decomposition of any solution of the problem can be established and on the other hand the finite element method is used to determinate the numerical results. Furthermore, the influence of soil parameters G_{p} and K_{p} on the displacement of the pious is studied numerically at any time t_{n}.
Paper's Title:
Orthogonal Collocation on Finite Elements Using Quintic Hermite Basis
Author(s):
P. Singh, N. Parumasur and C. Bansilal
University of KwaZuluNatal,
School of Mathematics Statistics and Computer Sciences,
Private Bag X54001,
Durban, 4000,
South Africa.
Email: 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) piecewisepolynomials and more accurate than the (third degree smooth) Bsplines basis. Various computational simulations are presented to demonstrate the computational efficiency and versatility of the OCFE method.
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 239556900,
Saudi
Arabia.
Email: sean.stewart@kaust.edu.sa
Abstract:
Integral representations of the Fibonacci numbers F_{kn + r} and the Lucas numbers L_{kn + r} are presented. Each is established using methods that rely on nothing beyond elementary integral calculus.
Paper's Title:
Fractional Integral Inequalities of HermiteHadamard Type for Pconvex and QuasiConvex 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.
Email: 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.
Email: mohammed.barmaki@uit.ac.ma
National School of Applied Sciences (ENSA),
University Ibn Tofail,
B.P 242 Kenitra 14000,
phone number : +212661403557,
Morocco.
Email: driss.gretete@uit.ac.ma
Abstract:
In this paper we consider the class of Pconvex and Quasiconvex stochastic processes on witch we apply a general class of generalized fractional integral operator in order to establish new integral inequalities of HermiteHadammard 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.
Paper's Title:
Generalized FugledePutnam Theorem and Orthogonality
Author(s):
A. Bachir and A. Sagres
Department of
Mathematics, Faculty of Science, King Khaled
University, Abha, P.O. Box 9004 Kingdom Saudi Arabia
bachir_ahmed@hotmail.com
sagres@hotmail.com
Abstract:
An asymmetric FugledePutnam’s theorem for dominant operators and phyponormal 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.
Paper's Title:
A Majorization Problem for the Subclass of pValently 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.
Paper's Title:
Norm Estimates for the Difference between Bochner’s Integral and the Convex Combination of Function’s Values
Author(s):
P. Cerone, Y.J. Cho, S.S. Dragomir, J.K. Kim, and S.S. Kim
School of
Computer Science and Mathematics,
Victoria University of Technology,
Po Box 14428, Mcmc 8001, Victoria, Australia.
pietro.cerone@vu.edu.au
URL:
http://rgmia.vu.edu.au/cerone/index.html
Department of
Mathematics Education, College of Education,
Gyeongsang National University, Chinju 660701, Korea
yjcho@nongae.gsnu.ac.kr
School of
Computer Science and Mathematics,
Victoria University of Technology,
Po Box 14428, Mcmc 8001, Victoria, Australia.
sever.dragomir@vu.edu.au
URL:
http://rgmia.vu.edu.au/SSDragomirWeb.html
Department of
Mathematics, Kyungnam University,
Masan,, Kyungnam 631701, Korea
jongkyuk@kyungnam.ac.kr
Department of
Mathematics, Dongeui University,
Pusan 614714, Korea
sskim@dongeui.ac.kr
Abstract:
Norm estimates are developed between the Bochner integral of a vectorvalued function in Banach spaces having the RadonNikodym property and the convex combination of function values taken on a division of the interval [a, b].
Paper's Title:
New Coincidence and Fixed Point Theorems for Strictly Contractive Hybrid Maps
Author(s):
S. L. Singh and Amal M. Hashim
21, Govind Nagar, Rishikesh 249201,
Ua, India
vedicmri@sancharnet.in
Dept. of Math., College of Science,
Univ. of Basarah,
Iraq.
Abstract:
The purpose of this paper is to study the (EA)property and noncompatible maps of a hybrid pair of singlevalued and multivalued maps in fixed point considerations. Such maps have the remarkable property that they need not be continuous at their common fixed points. We use this property to obtain some coincidence and fixed point theorems for strictly contractive hybrid maps without using their continuity and completeness or compactness of the space.
Paper's Title:
Multivalued Hemiequilibrium Problems
Author(s):
Muhammad Aslam Noor
Mathematics Department,
COMSATS Institute of Information Technology,
Sector H8/1, 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.
Paper's Title:
A general theory of decision making
Author(s):
Frank Hansen
Department of Economics,
University of Copenhagen,
Studiestraede 6, DK1455 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 nonadditive measures.
Paper's Title:
Logarithmically complete monotonicity properties for the gamma functions
Author(s):
ChaoPing Chen and Feng Qi
Department of Applied Mathematics and Informatics,
Research Institute of Applied Mathematics,
Henan Polytechnic University,
Jiaozuo City, Henan 454010,
China.
chenchaoping@hpu.edu.cn
Department of Applied Mathematics and Informatics,
Research Institute of Applied Mathematics,
Henan Polytechnic University,
Jiaozuo City, Henan 454010,
China.
qifeng@hpu.edu.cn
fengqi618@member.ams.org
Abstract:
Some logarithmically completely monotonic functions involving the gamma functions are presented. As a consequence, some known results are proved and refined.
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.
isacg@rmc.ca
Faculty of Mathematics and Computer Science,
BabesBolyai University,
3400 ClujNapoca,
Romania.
nemab@math.ubbcluj.ro
Abstract:
The notion of nuclear cone in locally convex spaces corresponds to the notion of well based cone in normed spaces. Using the bipolar theorem from locally convex spaces it is proved that every closed nuclear cone is a full nuclear cone. Thus every closed nuclear cone can be associated to a mapping from a family of continuous seminorms in the space to the topological dual of the space. The relation with Pareto efficiency is discussed.
Paper's Title:
On the Optimal Buckling Loads of Clamped Columns
Author(s):
Samir Karaa
Department of Mathematics and Statistics
Sultan Qaboos University, P.O. Box 36, Alkhod 123
Muscat, Sultanate of Oman
skaraa@squ.edu.om
URL: http://ajmaa.org/EditorsU/SKaraa.php
Abstract:
We consider the problem of determining the optimal shape of a clamped column of given length and volume, without minimum cross section constraints. We prove that the necessary condition of optimality derived by Olhoff and Rasmussen is sufficient when 0<α<1. The number alpha appears in Equation 2.1. For the case α =1 it is shown that the value 48 is optimal. We also determine the exact values of the optimal shape at the extremities, and take advantage of a robust nonlinear ordinary differential equation solver COLSYS to compute the optimal buckling load with a high accuracy.
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, VisvaBharati 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 timedependent, twodimensional incompressible nonlinear NavierStokes 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.
Paper's Title:
A Wallis Type Inequality and a Double Inequality for Probability Integral
Author(s):
Jian Cao, DaWei 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.
Paper's Title:
Normalized Truncated Levy models applied to the study of Financial Markets
Author(s):
M. C. Mariani, K. Martin, D. W. Dombrowski and D. Martinez
Department of Mathematical Sciences and Department of Finance,
New Mexico State University, P.O. Box 30001
Department 3MB Las Cruces, New Mexico 880038001
USA.
mmariani@nmsu.edu
kjmartin@nmsu.edu
Abstract:
This work is devoted to the study of the statistical properties of financial instruments from developed markets. We performed a new analysis of the behavior of companies corresponding to the DJIA index, and of the index itself, by using a normalized Truncated Levy walk model. We conclude that the Truncated Levy distribution describes perfectly the evolution of the companies and of the index near a crash.
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 qdifference equations. The results are illustrated with numerous examples.
Paper's Title:
Existence of Bounded Solutions for a Class of Strongly Nonlinear Elliptic Equations in OrliczSobolev 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 FezAtlas, Fez
Morocco
a.benkirane@menara.ma
ahmed.youssfi@caramail.com
Abstract:
We prove, in the setting of OrliczSobolev 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 Δ_{2}condition is needed for the considered Nfunctions.
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.
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
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.
Paper's Title:
On εsimultaneous 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://mathcs.aut.ac.ir/vaezpour
Abstract:
The purpose of this paper is to develop a theory of best simultaneous approximation to εsimultaneous approximation. We shall introduce the concept of εsimultaneous pseudo Chebyshev, εsimultaneous quasi Chebyshev and εsimultaneous weakly Chebyshev subspaces of a Banach space. Then, it will be determined under what conditions these subspaces are transmitted to and from quotient spaces.
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,
H4010 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 2homogeneous 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.
Paper's Title:
A Coincidence Theorem for Two Kakutani Maps
Author(s):
Mircea Balaj
Department of Mathematics,
University of Oradea,
410087, Oradea,
Romania.
mbalaj@uoradea.ro
Abstract:
In this paper we prove the following theorem: Let X be a nonempty compact convex set in a locally convex Hausdorff topological vector space, D be the set of its extremal points and F,T: X―◦X two Kakutani maps; if for each nonempty finite subset A of D and for any x ∈ coA, F (x) ∩ coA ≠ Ø, then F and T have a coincidence point. The proof of this theorem is given first in the case when X is a simplex, then when X is a polytope and finally in the general case. Several reformulations of this result are given in the last part of the paper.
Paper's Title:
Generalized Efficient Solutions to One Class of Vector Optimization Problems in Banach Space
Author(s):
Peter I. Kogut, Rosanna Manzo, and Igor V. Nechay
Department of Differential Equations,
Dnipropetrovsk National University,
Naukova str., 13,
49050 Dnipropetrovsk,
Ukraine
p.kogut@i.ua
Dipartimento di Ingegneria
Dell’informazione e Matematica Applicata,
Università di Salerno,
Via
Ponte
Don Melillo,
84084 Fisciano
(Sa),
Italy
manzo@diima.unisa.it
Department of Technical Cybernetics,
Dnipropetrovsk Technical University,
Acad. Lazarjan str., 2,
49010
Dnipropetrovsk,
Ukraine
i.nechay@i.ua
Abstract:
In this paper, we study vector optimization problems in Banach spaces for essentially nonlinear operator equations with additional control and state constraints. We assume that an objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. Using the penalization approach we derive both sufficient and necessary conditions for the existence of efficient solutions of the above problems. We also prove the existence of the socalled generalized efficient solutions via the scalarization of some penalized vector optimization problem.
Paper's Title:
On an Elliptic OverDetermined 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.
Abstract:
We extend the method of Weinberger for a
nonlinear overdetermined elliptic problem
in R^{2}.
We prove that the domain in consideration is a ball. The
tool of this investigation are maximum principles and Pfunctions.
Paper's Title:
Turan Type Inequalities for Some Special Functions
Author(s):
W. T. Sulaiman
Department of Computer Engineering,
College of Engineering,
University of Mosul,
Iraq
Abstract:
In this paper new results concerning the qpolygamma and qzeta functions are presented. Other generealizations of some known results are also obtained.
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 threedimensional 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.
Paper's Title:
TraubPotraType Method for SetValued Maps
Author(s):
Ioannis K. Argyros and Saïd Hilout
Cameron University,
Department of Mathematics Sciences,
Lawton, OK 73505,
USA
URL: http://www.cameron.edu/~ioannisa/
Poitiers University,
Laboratoire de Mathematiques et Applications,
Bd. Pierre et Marie Curie, Teleport 2, B.P. 30179,
86962 Futuroscope Chasseneuil Cedex,
France
said.hilout@math.univpoitiers.fr
http://wwwmath.univpoitiers.fr/~hilout/
Abstract:
We introduce a new iterative method for approximating a locally unique solution of variational inclusions in Banach spaces by using generalized divided differences of the first order. This method extends a method considered by Traub (in the scalar case) and by Potra (in the Banach spaces case) for solving nonlinear equations to variational inclusions. An existenceconvergence theorem and a radius of convergence are given under some conditions on divided differences operator and Lipschitzlike continuity property of setvalued mappings. The Rorder of the method is equal to the unique positive root of a certain cubic equation, which is $1.839..., and as such it compares favorably to related methods such as the Secant method which is only of order $1.618....
Paper's Title:
Weak solutions of non coercive stochastic NavierStokes equations in R^{2}
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 1538914,
Japan.
Email: stannat@math.tuberlin.de
Email: satoshi2@ms.utokyo.ac.jp
Abstract:
We prove existence of weak solutions of stochastic NavierStokes equations in R^{2} 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 R^{2}. 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 2DNavierStokes equations with periodic boundary conditions, where the periodicity is growing to infinity combined with a suitable spatial cutofftechnique.
Paper's Title:
On the Regularization of Hammerstein's type Operator Equations
Author(s):
E. Prempeh, I. OwusuMensah and K. PiesieFrimpong
Department of Mathematics,
KNUST, Kumasi
Ghana.
Department of Science Education,
University of Education,
Winneba
Department of Mathematics,
Presbyterian University College, Abetifi,
Ghana
Email: isaacowusumensah@gmail.com
Email: eprempeh.cos@knust.edu.gh
Email: 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.
Paper's Title:
Properties of qgamma and qbeta functions derived from the qGaussPólya inequalities
Author(s):
Sanja Varošanec
Department of Mathematics,
University of Zagreb,
Zagreb, Croatia
Email:
varosans@math.hr
Abstract:
We consider logconvexity and other properties of several functions related to qgamma and qbeta functions. These properties are consequences of the general inequality, socalled qanalogue of the GaussPólya inequality. Various inequalities involving these special functions are also given.
Paper's Title:
Stability of the DBar Reconstruction Method for Complex Conductivities
Author(s):
^{1}S. El Kontar, ^{1}T. El Arwadi, ^{1}H. Chrayteh, ^{2}J.M. SacÉpée
^{1}Department of Mathematics and
Computer Science,
Faculty of Science, Beirut Arab University,
P.O. Box: 115020, Beirut,
Lebanon.
Email: srs915@student.bau.edu.lb
^{2}Institut Élie Cartan de
Lorraine,
Université de Lorraine  Metz,
France.
Abstract:
In 2000, Francini solved the inverse conductivity problem for twicedifferentiable conductivities and permittivities. This solution was considered to be the first approach using Dbar 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 DBar equation gives the complex conductivity. In this paper, the stability of the DBar equation is studied via two approximations, t^{exp} and t^{B}, for the scattering transform. The study is based on rewriting the reconstruction method in terms of continuous operators. The conductivity is considered to be non smooth.
Paper's Title:
Generalized Weighted Trapezoid and Grüss Type Inequalities on Time Scales
Author(s):
Eze Raymond Nwaeze
Department of Mathematics,
Tuskegee University,
Tuskegee, AL 36088,
USA.
Email: enwaeze@mytu.tuskegee.edu
Abstract:
In this work, we obtain some new generalized weighted trapezoid and Grüss type inequalities on time scales for parameter functions. Our results give a broader generalization of the results due to Pachpatte in [14]. In addition, the continuous and discrete cases are also considered from which, other results are obtained.
Paper's Title:
Relation Between The Set Of Nondecreasing 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
Email:
qefsere.gjonbalaj@unipr.edu
Department of Engineering Mathematics,
Polytechnic University of Tirana, Tirana,
Albania.
Email: 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.
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.
Email:
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. 495508.]
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.
Email:
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 diseasefree equilibrium point and the endemic equilibrium point. The existence and global stability of equilibrium points depend on the basic reproduction number R_{0}. When R_{0} <1, only the diseasefree equilibrium point exists. If R_{0} >1, there are two equilibrium points, which are the diseasefree equilibrium point and the endemic equilibrium point. Based on the result of stability analysis, the diseasefree equilibrium point is globally asymptotically stable if R_{0} <1, while if R_{0} > 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.
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.
Email: 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 roundoff errors and finds the solution without any restrictive assumptions or discretization. We will introduce an appropriate initial approximation and furthermore, the residual error will be canceled in some points of the interval (RECP). Only a first order approximation of MSTHPM will be required, as compared to STHPM, which needs more iterations for the same cases of study. After comparing figures between approximate, MSTHPM, STHPM and numerical solutions, it is found through the solutions we have obtained that they are highly accurate, indicating that the MSTHPM is very effective, simple and can be used to solve other types of nonlinear boundary value problems (BVPs).
Paper's Title:
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
Email: 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 RungeKutta 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 RungeKutta methods. This article takes the first step by investigating the performance of passive extrapolation for DIMSIMs type2 methods. In the variable stepsize and order codes, order2 and order3 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.
Paper's Title:
On The Degree of Approximation of Periodic Functions from Lipschitz and Those from Generalized Lipschitz Classes
Author(s):
Xhevat Z. Krasniqi
Faculty of Education,
University of Prishtina "Hasan Prishtina",
Avenue "Mother Theresa " no. 5, Prishtinë
10000,
Republic of Kosovo.
Email: xhevat.krasniqi@unipr.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.
Paper's Title:
An Efficient Modification of Differential Transform Method for Solving Integral and Integrodifferential Equations
Author(s):
S. AlAhmad, Ibrahim Mohammed Sulaiman^{*}, and M. Mamat
Faculty of Informatics and Computing,
Universiti Sultan Zainal Abidin,
Terengganu, Besut Campus, 22200,
Malaysia.
Email: Alahmad.shadi@yahoo.com,
^{*}sulaimanib@unisza.edu.my,
must@unisza.edu.my
Abstract:
In this paper, classes of integral and integrodifferential 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 integrodifferential equations.
Paper's Title:
Numerical Approximation by the Method of Lines with Finitevolume 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.
Email: bondami@gmail.com
Abstract:
In this paper we are interested in the numerical approximation of a twodimensional 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 socalled 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.
Paper's Title:
Generalized Von NeumannJordan 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.
Email: hairur@mat.uinmalang.ac.id
Analysis and Geometry Group,
Faculty of Mathematics and Natural Sciences,
Bandung Institute of Technology, Bandung 40132,
Indonesia.
Email: 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 NeumannJordan constant, modified Von NeumannJordan 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 NeumannJordan constant for Morrey spaces and small Morrey spaces.
Paper's Title:
Algorithms for Nonlinear Problems Involving Strictly Pseudocontractive Mappings
Author(s):
Mathew Olajiire Aibinu^{1}, Surendra Colin Thakur^{2}, Sibusiso Moyo^{3}
^{1}Institute for Systems Science
& KZN ESkill CoLab,
Durban University of Technology,
Durban 4000,
South Africa.
^{1}DSINRF
Centre of Excellence in Mathematical and Statistical Sciences (CoEMaSS),
Johannesburg,
South Africa.
Email: moaibinu@yahoo.com
mathewa@dut.ac.za
^{2} KZN ESkill CoLab,
Durban University of Technology,
Durban 4000,
South Africa.
Email: thakur@dut.ac.za
^{3}Institute for Systems Science & Office of the DVC Research,
Innovation & Engagement Milena Court,
Durban University of Technology,
Durban 4000,
South Africa.
Email: 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 μstrictly 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.
Paper's Title:
Improved Oscillation Criteria of SecondOrder Advanced Noncanonical Difference Equation
Author(s):
G. E. Chatzarakis^{1}, N. Indrajith^{2}, S. L. Panetsos^{1}, E. Thandapani^{3}
^{1}Department
of Electrical and Electronic Engineering Educators
School of Pedagogical and Technological Education,
Marousi 15122, Athens,
Greece.
Email: gea.xatz@aspete.gr,
geaxatz@otenet.gr
spanetsos@aspete.gr
^{2}Department
of Mathematics,
Presidency College, Chennai  600 005,
India.
Email: indrajithna@gmail.com
^{3}Ramanujan
Institute for Advanced Study in Mathematics,
University of Madras Chennai  600 005,
India.
Email: ethandapani@yahoo.co.in
Abstract:
Employing monotonic properties of nonoscillatory solutions, we derive some new oscillation criteria for the secondorder advanced noncanonical difference equation
Our results extend and improve the earlier ones. The outcome is illustrated via some particular difference equations.
Paper's Title:
Introducing the PicardS3 Iteration for Fixed Points
Author(s):
Pravin Singh, Virath Singh and Shivani Singh
University of KwaZuluNatal,
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.
Email: 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.
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 Yatsen University,
Guangzhou, 510275,
P.R. China.
Email: dudd5@mail2.sysu.edu.cn
Department of Mathematics,
Sun Yatsen University,
Guangzhou, 510275,
P.R. China.
Email: stslyj@mail.sysu.edu.cn
Abstract:
In this paper, we shall consider two new constants δ_{B}(X) and ρ_{B}(X), which are the modulus of convexity and the modulus of smoothness related to Birkhoff orthogonality, respectively. The connections between these two constants and other wellknown constants are established by some equalities and inequalities. Meanwhile, we obtain two characterizations of Hilbert spaces in terms of these two constants, study the relationships between the constants δ_{B}(X), ρ_{B}(X) and the fixed point property for nonexpansive mappings. Furthermore, we also give a characterization of the Radon plane with affine regular hexagonal unit sphere.
Paper's Title:
A Unifying View of Some Banach Algebras
Author(s):
R. Kantrowitz
Mathematics & Statistics Department,
Hamilton College,
198 College Hill Road,
Clinton, NY 13323, USA.
Email: rkantrow@hamilton.edu
Abstract:
The purpose of this article is to shed light on a unifying framework for some normed algebras and, in particular, for some Banach algebras. The focus is on linear operators T between normed algebras X and Y and specified subalgebras A of Y. When the action of T on products in X satisfies a certain operative equation, the subspace T^{1}(A) is stable under the multiplication of X and is readily equipped with a family of canonical submultiplicative norms. It turns out that many familiar and important spaces are encompassed under this versatile perspective, and we offer a sampling of several such. In this sense, the article presents an alternative lens through which to view a host of normed algebras. Moreover, recognition that a normed linear space conforms to this general structure provides another avenue to confirming that it is at once stable under multiplication and also outfitted with an abundance of equivalent submultiplicative norms.
Paper's Title:
Metric Functionals for the Hästö Metric
Author(s):
G. Bettencourt and S. Mendes
Departamento de Matemática,
Universidade da Beira Interior 
Covilhã Portugal,
Centro de Matemática e Aplicações
Universidade da Beira Interior 
Covilhã Portugal.
Email: gastao@ubi.pt
ISCTE  University Institute of Lisbon  Lisbon Portugal,
Centro de Matemática e Aplicações
Universidade da Beira Interior 
Covilhã Portugal.
Email: sergio.mendes@iscteiul.pt
Abstract:
In 2002, new classes of weighted metrics on R^{n} were introduced by Peter Hästö. In this article we compute the metric functionals for such classes of metrics.
Paper's Title:
Constraint Qualifications for Multiobjective Programming Problems on Hadamard Manifolds
Author(s):
Arnav Ghosh, Balendu Bhooshan Upadhyay and I.M. StancuMinasian
Department of Mathematics,
Indian Institute of Technology Patna,
Patna,
India.
Email: arnav_2021ma09@iitp.ac.in
Department of Mathematics,
Indian Institute of Technology Patna,
Patna,
India.
Email: bhooshan@iitp.ac.in
"Gheorghe MihocCaius Iacob" Institute of
Mathematical Statistics and Applied Mathematics of the Romanian Academy,
Bucharest,
Romania.
Email: 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 KarushKuhnTucker 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, Cottletype CQ, Slatertype CQ, linear CQ, linear objective CQ and MangasarianFromovitz 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.
Paper's Title:
Some Ostrowski Type Inequalities for Two CosIntegral 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.
DSTNRF 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.
Email: 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 cosintegral transforms
and
We provide in this paper some upper bounds for the quantities
and
for
x ∈ [ a,b], in terms of the pnorms of the derivative
f ' for absolutely continuous functions f:[a,b] ⊂[0,π]→C.
Applications for approximating Steklov cosaverage functions and Steklov
split cosaverage functions are also provided.
Paper's Title:
FeketeSzegö Inequality for Certain Class of Analytic Functions
Author(s):
V. Ravichandran, Maslina Darus, M. Hussain Khan, and K. G. Subramanian
School of
Mathematical Sciences, Universiti Sains Malaysia,
11800 Usm, Penang, Malaysia
vravi@cs.usm.my
School of
Mathematical Sciences, Faculty of Sciences and Technology,
Ukm, Banki 43600, Malaysia
maslina@pkrisc.cc.ukm.my
Department of
Mathematics, Islamiah College,
Vaniambadi 635 751, India
Department of
Mathematics, Madras Christian College, Tambaram,
Chennai 600 059, India
kgsmani@vsnl.net
Abstract:
In this present investigation, the authors obtain FeketeSzegö 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 FeketeSzegö inequality for a class of functions defined through fractional derivatives. Also we obtain FeketeSzegö inequality for the inverse functions.
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 variationallike inequality problem and generalized vector equilibrium problem. The results of this paper generalize some known results in the literature.
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.
Paper's Title:
Note on the Rank of Birkhoff Interpolation
Author(s):
J. RubióMassegú
Applied Mathematics III, Universitat Politècnica de Catalunya,
Colom 1, 08222, Terrassa,
Spain
josep.rubio@upc.edu
Abstract:
The relationship between a variant of the rank of a univariate Birkhoff interpolation problem, called normal rank, and other numbers of interest associated to the interpolation problem is studied.
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 singlevalued and two multivalued operators in symmetric spaces. We derive fixed point theorems and discuss some special cases and applications.
Paper's Title:
Generalized Hypergeometric Functions Defined on the Class of Univalent Functions
Author(s):
N. Marikkannan, A. Gangadharan and C. Ganesamoorthy
Department of Applied Mathematics,
Sri Venkateswara College of Engineering,
Sriperumbudur 602105,
India.
mari@svce.ac.in
Department of Applied mathematics,
Sri Venkateswara College of Engineering,
Sriperumbudur 602105,
India.
ganga@svce.ac.in
Department of Mathematics,
Alagappa university,
Karaikudi,
India.
ganesamoorthyc@yahoo.com
Abstract:
Let A denotes the class of all analytic functions f(z), normalized by the condition f'(0)1=f(0)=0 defined on the open unit disk Δ and S be the subclass of A containing univalent functions of A. In this paper, we find the sufficient conditions for hypergeometric functions defined on S to be in certain subclasses of A, like kUCV, kST
Paper's Title:
A Coefficient Inequality For Certain Subclasses of Analytic Functions Related to Complex Order
Author(s):
B. Srutha Keerthi, B. Adolf Stephen and S. Sivasubramanian
Department Of Applied Mathematics, Sri Venkateswara College Of Engineering, Anna University,
Sriperumbudur, Chennai  602 105,
India.
laya@svce.ac.in
Department of Mathematics, Madras Christian College,
Chennai  600059,
India
adolfmcc2003@yahoo.co.in
Department of Mathematics, College of Engineering, Anna University,
Tamilnadu, Chennai  600 025,
India.
sivasaisastha@rediffmail.com
Abstract:
In this present investigation, the authors obtain coefficient inequality for certain normalized analytic functions of complex order f(z) defined on the open unit disk for which _{ } (_{ } and _{} be a complex number) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions of complex order defined by convolution are given. As a special case of this result, coefficient inequality for a class of functions defined through fractional derivatives is obtained. The motivation of this paper is to give a generalization of the coefficient inequalities of the subclasses of starlike and convex functions of complex order.
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 MoorePenrose inverse and the weighted MoorePenrose 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 MoorePenrose inverse, the MoorePenrose 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 _{ }.
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.
nsweilam@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.
Paper's Title:
On Sandwich Theorems for Certain Subclass of Analytic Functions Involving DziokSrivastava Operator
Author(s):
T. N. Shanmugam, M. P. Jeyarama and A. Singaravelu
Department of Mathematics
College of Engineering, Anna University
Chennai  600 025,
India
drtns2001@yahoo.com
Department of Mathematics
Easwari Engineering College
Ramapuram, Chennai  600089
Tamilnadu, India
jeyaramanmp@yahoo.co.i
Department of Mathematics
Valliammai Engineering College
Chennai  603203
Tamilnadu, India.
asing59@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 DziokSrivastava operator. Relevant connections of the results, which are presented in this paper, with various known results are also considered.
Paper's Title:
On a Subclass of Uniformly Convex Functions Defined by the DziokSrivastava 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 DziokSrivastava operator, we define a new subclass T^{l}_{m}([α_{1}];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 closetoconvexity, starlikeness and convexity for functions belonging to the class T^{l}_{m}([α_{1}];α,β) . We consider integral operators associated with functions belonging to the class H^{l}_{m}([α_{1}];α,β) defined via the DziokSrivastava operator. We also obtain several results for the modified Hadamard products of functions belonging to the class T^{l}_{m}([α_{1}];α,β) and we obtain properties associated with generalized fractional calculus operators.
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 pvalent 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.
Paper's Title:
On a Method of Proving the HyersUlam Stability of Functional Equations on Restricted Domains
Author(s):
Janusz Brzdęk
Department of Mathematics
Pedagogical University Podchorąźych 2,
30084 Kraków,
Poland
jbrzdek@ap.krakow.pl
Abstract:
We show that generalizations of some (classical) results on the HyersUlam 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
Paper's Title:
On the Generalized Stability and Asymptotic Behavior of Quadratic Mappings
Author(s):
HarkMahn Kim, SangBaek Lee and Eunyoung Son
Department of Mathematics
Chungnam National University
Daejeon,
305764,
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.
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 133791,
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 HyersUlam stability of homomorphisms in Banach algebras and of derivations on Banach algebras for the Cauchy functional equation.
Paper's Title:
Purely Unrectifiable Sets with Large Projections
Author(s):
Harold R. Parks
Department of Mathematics,
Oregon State University,
Corvallis, Oregon 973314605,
USA
parks@math.oregonstate.edu
URL: http://www.math.oregonstate.edu/people/view/parks/
Abstract:
For n≥2, we give a construction of a compact subset of that is dispersed enough that it is purely unrectifiable, but that nonetheless has an orthogonal projection that hits every point of an (n1)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 1dimensional Hausdorff measure.
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).
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.tcom.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.
Paper's Title:
Trapping of Water Waves By Underwater Ridges
Author(s):
^{1}A. M. Marin, ^{ 1}R. D. Ortiz and ^{2}J. A. RodriguezCeballos.
^{1}Facultad de Ciencias Exactas y Naturales
Universidad de Cartagena
Sede Piedra de Bolivar, Avenida del Consulado
Cartagena de Indias, Bolivar,
Colombia.
^{2}Instituto 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 wellknown, 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 15071550)).
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 235284), in order to solve
them.
Paper's Title:
A Generalization of a Trace Inequality for Positive Definite Matrices
Author(s):
E. V. Belmega, M. Jungers, and S. Lasaulce
Université ParisSud Xi, SUPELEC,
Laboratoire Des Signaux Et Systèmes,
GifSurYvette,
France.
belmega@lss.supelec.fr
http://veronica.belmega.lss.supelec.fr
CNRS, ENSEM, CRAN, Vandoeuvre,
France.
marc.jungers@cran.uhpnancy.fr
http://perso.ensem.inplnancy.fr/Marc.Jungers/
CNRS, SUPELEC, Laboratoire des Signaux et
Systèmes,
GifSurYvette,
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, A_{1}, B_{1} are any positive definite matrices and A_{k}, B_{k} for all k∈{2,...,k}, are any positive semidefinite matrices.
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.
Paper's Title:
Fejértype Inequalities
Author(s):
Nicuşor Minculete and FlaviaCorina 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, RO200585,
Romania
fcmitroi@yahoo.com
Abstract:
The aim of this paper is to present some new Fejértype results for convex functions. Improvements of Young's inequality (the arithmeticgeometric mean inequality) and other applications to special means are pointed as well.
Paper's Title:
Renormalized Solutions for Nonlinear Parabolic Equation with Lower Order Terms
Author(s):
A. Aberqi^{1}, J. Bennouna^{1}, M. Mekkour^{1} and H. Redwane^{2}
^{1}Université Sidi Mohammed Ben
Abdellah,
Département de Mathématiques,
Laboratoire LAMA, Faculté des Sciences DharMahrez,
B.P 1796 Atlas Fés,
Morocco.
^{2}Faculté des Sciences
Juridiques, Economiques et Sociales,
Université Hassan 1, B.P. 784. Settat,
Morocco.
aberqiahmed@ya_hoo.fr
jbennouna@hotmail.com
mekkour.mounir@yahoo.fr
redwane_hicham@yahoo.fr
Abstract:
In this paper, we study the existence of renormalized solutions for the nonlinear parabolic problem: ,where the right side belongs to L^{1}(Ω×(0,T)) and b(u) is unbounded function of u, the term div(a(x,t,u,∇u)) is a LerayLions operator and the function φ is a nonlinear lower order and satisfy only the growth condition.
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.
Email: laharouch@gmail.com
Université Sidi Mohammed Ben Abdellah
Faculté des Sciences DharMahraz
B.P 1796 Atlas Fès,
Maroc.
Email: jbennouna@hotmail.com
Email: kadabouajaja@hotmail.com
Abstract:
We prove the existence and the regularity of minima for a functional defined on a suitable Sobolev space.
Paper's Title:
Some Double λConvergent Sequence Spaces Over nNormed Spaces
Author(s):
Kuldip Raj, Renu Anand and Seema Jamwal
School of Mathematics,
Shri Mata Vaishno Devi University Katra182320,
Jammu and Kashmir,
India.
Email: kuldipraj68@gmail.com, renuanand71@gmail.com, seemajamwal8@gmail.com
Abstract:
In this paper we introduce some double generalized λconvergent sequence spaces over nnormed spaces defined by MusielakOrlicz function M = (M_{k,l}). We also made an attempt to study some topological and algebraic properties of these sequence spaces.
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.
Email: dr_juma@hotmail.com
Department of Mathematics,
Tikrit University, Tikrit,
Iraq.
URL: husamaddin@gmail.com
Abstract:
In this paper, we have introduced and studied new operator $Q^{k}_{λ,m,γ} by the Hadamard product (or convolution) of two linear operators D^{k}_{λ} and I_{m,γ}, then using this operator to study and investigate a new subclass of meromorphic functions of Janowski type, giving the coefficient bounds, a sufficient condition for a function to belong to the considered class and also a convolution property. The results presented provide generalizations of results given in earlier works.
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.
Email:
artionkashuri@gmail.com
Email: 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 GaussJacobi 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 RiemannLiouville fractional integrals are established.
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
Gokisocho, Showaku, Nagoya
Aichi, 4668555, Japan.
Email: 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.
Paper's Title:
A Note on Divergent Fourier Series and λPermutations
Author(s):
A. Castillo, J. Chavez and H. Kim
Tufts University,
Department of Mathematics,
Medford, MA 02155,
USA
Email: angel.castillo@tufts.edu
Texas Tech University,
Department of Mathematics and Statistics,
Lubbock, TX 79409,
USA
Email: josechavez5@my.unt.edu
University of MichiganDearborn,
Department of Mathematics and Statistics,
Dearborn, MI 48128,
USA.
Email: 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 λpermutation.
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.
Email: a.guechi2017@gmail.com
Email: a.rahmoune@univbba.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 spectralcollocation method to solve the mapped integral equation in the finite interval. Numerical examples are presented to illustrate the accuracy of the method.
Paper's Title:
EulerMaclaurin Formulas for Functions of Bounded Variation
Author(s):
G. De Marco, M. De Zotti, C. Mariconda
Dipartimento di Matematica Tullio LeviCivita,
Universita degli Studi di Padova
Via Trieste 63, Padova 35121,
Italy.
Email: carlo.mariconda@unipd.it
URL: http://www.math.unipd.it
Abstract:
The firstorder EulerMaclaurin 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.
Paper's Title:
Iterative Algorithm for Split Generalized Mixed Equilibrium Problem Involving Relaxed Monotone Mappings in Real Hilbert Spaces
Author(s):
^{1}U.A. Osisiogu, F.L. Adum, and ^{2}C. Izuchukwu
^{1}Department of Mathematics and
Computer Science,
Ebonyi State University, Abakaliki,
Nigeria.
Email: uosisiogu@gmail.com,
adumson2@yahoo.com
^{2}School of Mathematics,
Statistics and Computer Science,
University of KwaZuluNatal, Durban,
South Africa.
Email: 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.
Paper's Title:
The Influence of Fluid Pressure in Macromechanical Cochlear Model
Author(s):
F. E. Aboulkhouatem^{1}, F. Kouilily^{1}, N. Achtaich^{1}, N. Yousfi^{1} and M. El Khasmi^{2}
^{1}Department
of Mathematics and Computer Science, Faculty of Sciences
Ben M'sik, Hassan II University, Casablanca,
Morocco.
^{2}Department
of Biology, Faculty of Sciences
Ben M'sik, Hassan II University, Casablanca,
Morocco.
Email:
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.
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 380701,
Republic of Korea.
Department of Mathematics Education,
Wonkwang University, Iksan, 570749,
Republic of Korea.
Department of Mathematics,
Vedant College of Engineering and Technology (Rajasthan Technical University),
Bundi323021, Rajasthan,
India.
Email: sjun@kku.ac.kr, iki@wku.ac.kr, arjunkumarrathie@gmail.com
Abstract:
Very recently MasjedJamei and Koepf established interesting and useful generalizations of various classical summation theorems for the _{2}F_{1}, _{3}F_{2}, _{4}F_{3}, _{5}F_{4} and _{6}F_{5} 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.
Paper's Title:
Cubic Alternating Harmonic Number Sums
Author(s):
Anthony Sofo
Victoria University,
College of Engineering and Science,
Melbourne City,
Australia.
Email:
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.
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 AlRazak, and Muna M. Mustafa
Mathematics Department,
College of Sciences for Women,
University of Baghdad, Baghdad,
Iraq.
Email:
Nadiamj_math@csw.uobaghdad.edu.iq
Abstract:
In this paper, we formulate three mathematical models using spline functions, such as linear, quadratic and cubic functions to approximate the mathematical model for incoming water to some dams. We will implement this model on dams of both rivers; dams on the Tigris are Mosul and Amara while dams on the Euphrates are Hadetha and AlHindya.
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, NdufuAlike,
Nigeria.
Email: omenyi.louis@funai.edu.ng,
michael.uchenna@funai.edu.ng
URL: http://www.funai.edu.ng
Abstract:
In this paper, an exposition of the central concept of global analysis on a Riemannan manifold is given. We extend the theory of smooth vector fields from open subsets of Euclidean space to Riemannan manifolds. Specifically, we prove that a Riemannian manifold admits a unique solution for a system of ordinary differential equations generated by the flow of smooth tangent vectors. The idea of partial differential equations on Riemannian manifold is highlighted on the unit sphere.
Paper's Title:
Simplicial (co)homology of Band Semigroup
Author(s):
Yasser Farhat
Academic Support Department,
Abu Dhabi Polytechnic,
P.O. Box 111499, Abu Dhabi,
UAE.
Email: yasser.farhat@adpoly.ac.ae, farhat.yasser.1@gmail.com
Abstract:
We consider the Banach algebra l^{1}(S), with convolution, where S is a band semigroup. We prove directly, without using the cyclic cohomology, that the simplicial cohomology groups H^{n}(l^{1}(S), l^{1}(S)^{*}) vanish for all n≥1. This proceeds in three steps. In each step, we introduce a bounded linear map. By iteration in each step, we achieve our goal.
Paper's Title:
Some Properties of (co)homology of Lie Algebra
Author(s):
Alaa Hassan Noreldeen Mohamed, Hegagi Mohamed Ali, Samar Aboquota
Department of Mathematics,
Faculty of
Science,
Aswan University, Aswan,
Egypt.
Email: ala2222000@yahoo.com
hegagi_math@aswu.edu.eg
scientist_samar@yahoo.com
Abstract:
Lie algebra is one of the important types of algebras. Here, we studied lie algebra and discussed its properties. Moreover, we define the Dihedral homology of lie algebra and prove some relations among Hochschild, Cyclic and Dihedral homology of lie algebra. Finally, we prove the Mayervetories sequence on Dihedral homology of lie algebra and proved that .
Paper's Title:
Optimization Techniques on Affine Differential Manifolds
Author(s):
Ali S Rasheed, Faik Mayah and Ahmed A H ALJumaili
Ministry of Higher Education and
Scientific Research,
Iraq.
Email: ahmedhashem@gmail.com
Department of Physics, College of
Sciences,
University of Wasit,
Iraq.
Email: 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 selfconcordant 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 nonRiemannian schemes on manifolds.
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.
Email: athirachandri@gmail.com
Department of Mathematical and
Computational Sciences,
National Institute of Technology Karnataka,
Surathkal, Mangaluru 575 025,
India.
Email:sam@nitk.edu.in
Department of Mathematics,
University College of Engineering Arni,
Anna University, Arni 632 326,
India.
Email: 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.
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.
Email: rajkmc@gmail.com
Department of Mathematics,
University of Delhi,
Delhi,
India.
Email: 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.
Paper's Title:
Semivectorial Bilevel Optimization on AffineFinslerMetric Manifolds
Author(s):
Faik Mayah^{1}, Ali S Rasheed^{2} and Naseif J. Al Jawari^{3}
^{1}Department of Physics,
College of Sciences,
University of Wasit,
Iraq.
Email: faik.mayah@gmail.com
^{2}Ministry of Higher Education and Scientific Research,
Iraq.
Email: ali.math2018@yahoo.com
ahmedhashem@gmail.com
^{3}Dept.
of Mathematics,
College of Science,
Mustansiriyah University, Baghdad,
Iraq.
Email: 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, twoperson 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.
Paper's Title:
Oscillatory Behavior of SecondOrder NonCanonical Retarded Difference Equations
Author(s):
G.E. Chatzarakis^{1}, N. Indrajith^{2}, E. Thandapani^{3} and K.S. Vidhyaa^{4}
^{1}Department
of Electrical and Electronic Engineering Educators,
School of Pedagogical and Technological Education,
Marousi 15122, Athens,
Greece.
Email: gea.xatz@aspete.gr,
geaxatz@otenet.gr
^{2}Department
of Mathematics,
Presidency College, Chennai  600 005,
India.
Email: indrajithna@gmail.com
^{3}Ramanujan
Institute for Advanced Study in Mathematics,
University of Madras,
Chennai  600 005,
India.
Email: ethandapani@yahoo.co.in
^{4}Department of
Mathematics,
SRM Easwari Engineering College,
Chennai600089,
India.
Email: vidyacertain@gmail.com
Abstract:
Using monotonic properties of nonoscillatory solutions, we obtain new oscillatory criteria for the secondorder noncanonical difference equation with retarded argument
Our oscillation results improve and extend the earlier ones. Examples illustrating the results are provided.
Paper's Title:
The Boundedness of Gradient Solutions of PLaplacian Type
Author(s):
Corina Karim, Khoirunisa, Ratno Bagus Edy Wibowo
Department of Mathematics,
Universitas Brawijaya,
Veteran Street, Malang,
Indonesia.
Email: 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 pLaplacian systems only in the singular case. The Lebesgue space for initial data belong to guarantee the local boundedness of gradient solutions.
Paper's Title:
Application of Chebyshev Polynomials to VolterraFredholm Integral Equations
Author(s):
Aissa Lakhal, Mostefa Nadir and Mohamed Nasseh Nadir
Department of Mathematics,
Faculty of Mathematics and
Informatics,
University of Msila,
Algeria.
Email:
aissa.lakhal@univmsila.dz
mostefa.nadir@univmsila.dz
nadir.mohamednasseh@yahoo.com
URL: https://www.mostefanadir.com
Abstract:
The goal of this work is to examine the numerical solution of linear VolterraFredholm integral equations of the second kind using the first, second, third and fourth Chebyshev polynomials. Noting that, the approximate solution is given in the form of series which converges to the exact one. Numerical examples are compared with other methods, in order to prove the applicability and the efficiency of this technical.
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.
Email: 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 singlevalued 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.
Paper's Title:
Lozi Maps With Max Function and its Application
Author(s):
Abdellah Menasri
Higher National School of Forests,
Khenchela,
Algeria.
Email: 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 R^{2}. This is a family model that allows us to study several new piecewisesmooth maps. We demonstrate that these models converge to a robust chaotic attractor and give some applications of these models in the real world.
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,
Chennai603203,
India.
Email: nirmalat@srmist.edu.in
URL:
https://www.srmist.edu.in/faculty/drtnirmala/
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 predatorprey model.
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, 570749,
Korea.
Email: iki@wku.ac.kr
Department of Mathematics Education,
Wonkwang University,
Iksan, 570749,
Korea.
Email: 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.
Paper's Title:
The Automatic Continuity of NHomomorphisms in Certain *Banach Algebras
Author(s):
M. Aboulekhlef, Y. Tidli
Laboratory of Applied Mathematics and
Information and Communication Technology
Polydisciplinary Faculty of Khouribga
University of Sultan Moulay Slimane
Morocco.
Email: aboulekhlef@gmail.com
y.tidli@gmail.com
Abstract:
In this study, we prove the automatic continuity of surjective nhomomorphism between complete pnormed algebras. We show also that if Α and Β are complete *pnormed algebras, Β is *simple and ψ: Α → Β is a surjective nhomomorphism under certain conditions, then ψ is continuous.
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.Medchal500 078, Telangana,
India.
Email:
alphonse@hyderabad.bitspilani.ac.in
p20180442@hyderabad.bitspilani.ac.in
URL:
https://www.bitspilani.ac.in/hyderabad/amichaelalphonse
https://www.bitspilani.ac.in/research_scholars/srisaktiswarupanupindi
Abstract:
In this paper, we prove strong type inequality for maximal commutator of singular operator on weighted lp spaces. Using these results we prove strong type inequality for the maximal commutator of singular operator on variable exponent sequence spaces. Using CalderonCoifmanWeiss transference principle we prove strong type inequality for maximal ergodic commutator of singular operator on a probability space equipped with measure preserving transformation U.
Paper's Title:
Long Time Behavior for a Viscoelastic Problem with a Positive Definite Kernel
Author(s):
Nassereddine Tatar
King Fahd
University of Petroleum and Mineral, Department of Mathematical Sciences,
Dhahran, 31261 Saudi Arabia
tatarn@kfupm.edu.sa
Abstract:
We study the asymptotic behavior of solutions for an integrodifferential 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.
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 3768515, Japan
matsuura@me.gunmau.ac.jp
Department of Mathematics, Faculty of Engineering,
Gunma University, Kiryu 3768515, Japan
ssaitoh@math.sci.gunmau.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.
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 HyersUlam 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.
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 _{}
Paper's Title:
An alternative proof of monotonicity for the extended mean values
Author(s):
ChaoPing 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.
Paper's Title:
Reverse of Martin's Inequality
Author(s):
ChaoPing 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.
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 pvalent analytic functions defined through a linear operator.
Paper's Title:
Weak Solution for Hyperbolic Equations with a NonLocal Condition
Author(s):
Lazhar Bougoffa
King Khalid
University, Faculty of Science, Department of Mathematics,
P.O.Box 9004, Abha, Saudi Arabia
abogafah@kku.edu.sa
Abstract:
In this paper, we study hyperbolic equations with a nonlocal 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.
Paper's Title:
Orthogonality and εOrthogonality 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 εorthogonality 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.
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),
54792Lahore, 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.
Paper's Title:
The successive approximations method and error estimation in terms of at most the first derivative for delay ordinary differential equations
Author(s):
Alexandru Mihai Bica
Department of Mathematics,
University of Oradea,
Str. Armatei Romane no.5,
410087, Oradea,
Romania
smbica@yahoo.com
abica@uoradea.ro
Abstract:
We present here a numerical method for first order delay ordinary differential equations, which use the Banach's fixed point theorem, the sequence of successive approximations and the trapezoidal quadrature rule. The error estimation of the method uses a recent result of P. Cerone and S.S. Dragomir about the remainder of the trapezoidal quadrature rule for Lipchitzian functions and for functions with continuous first derivative.
Paper's Title:
Boundedness for VectorValued Multilinear Singular Integral Operators on TriebelLizorkin 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 vectorvalued multilinear operators associated to certain fractional singular integral operators on TriebelLizorkin space are obtained. The operators include CalderónZygmund singular integral operator and fractional integral operator.
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 BesselLaguerre 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 BesselLaguerre Weyl transform.
Paper's Title:
qNorms 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 qnorm. We establish that every qnorm is a norm in the usual sense, and that the converse is true as well.
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 twodimensional inhomogeneous elastic state in the curvilinear rectangle _{}_{} where _{} denote plane polar coordinates. Such an archlike region is maintained in equilibrium under selfequilibrated traction applied on the edge _{} while the other three edges _{}_{} and _{} are traction free. Our aim is to derive some explicit spatial exponential decay bounds for the specific Airy stress function and its derivatives. Two types of smoothly varying inhomogeneity are considered: (i) the elastic moduli vary smoothly with the polar angle, (ii) they vary smoothly with the polar distance. Such types of smoothly varying inhomogeneous elastic materials provide a model for technological important functionally graded materials. The results of the present paper prove how the spatial decay rate varies with the constitutive profile.
Paper's Title:
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@univpau.fr
URL: http://www.univpau.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, ... , n1.
Paper's Title:
pvalent 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.
Paper's Title:
On the FeketeSzegő Inequality for Some Subclasses of Analytic Functions
Author(s):
T.N. Shanmugam and A. Singaravelu
Department of Mathematics,
College of Engineering,
Anna University, Chennai600 025,
Tamilnadu, India
shan@annauniv.edu
Department of Mathematics,
Valliammai Engineering College,
Chennai603 203,
Tamilnadu, India
sivasaisastha@rediffmail.com
Abstract:
In this present investigation, the authors obtainFeketeSzegő'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, FeketeSzegő's inequality for a class of functions defined through fractional derivatives is also obtained.
Paper's Title:
A Stability of the Gtype Functional Equation
Author(s):
Gwang Hui Kim
Department of Mathematics, Kangnam University
Suwon 449702, Korea.
ghkim@kangnam.ac.kr
Abstract:
We will investigate the stability in the sense of Găvruţă for the Gtype 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 Gfunction equation.
Paper's Title:
Necessary and Sufficient Conditions for Uniform Convergence and Boundedness of a General Class of Sine Series
Author(s):
Laszlo Leindler
Bolyai Institute, University of Szeged,
Aradi Vértanúk tere 1,
H6720 Szeged,
Hungary.
leindler@math.uszeged.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.
Paper's Title:
Generalizations of HermiteHadamard's Inequalities for LogConvex Functions
Author(s):
AiJun Li
School of Mathematics and Informatics,
Henan Polytechnic University,
Jiaozuo City, Henan Province,
454010, China.
liaijun72@163.com
Abstract:
In this article, HermiteHadamard's inequalities are extended in terms of the weighted power mean and logconvex function. Several refinements, generalizations and related inequalities are obtained.
Paper's Title:
Power and EulerLagrange 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 EulerLagrange 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 EulerLagrange norm and that the converse is true under certain condition.
Paper's Title:
Existence of Solutions for Third Order Nonlinear Boundary Value Problems
Author(s):
Yue Hu and Zuodong Yang
School of Mathematics and Computer Science, Nanjing Normal University, Jiangsu Nanjing 210097,
China.
huu3y2@163.com
College of Zhongbei, Nanjing Normal University, Jiangsu Nanjing 210046,
China.
zdyang_jin@263.net
yangzuodong@njnu.edu.cn
Abstract:
In this paper, the existence of solution for a class of third order quasilinear ordinary differential equations with nonlinear boundary value problems
(Φ_{p}(u"))'=f(t,u,u',u"), u(0)=A, u'(0)=B, R(u'(1),u"(1))=0
is established. The results are obtained by using upper and lower solution methods.
Paper's Title:
Two Classes of Completely Monotonic Functions Involving Gamma and Polygamma Functions
Author(s):
BaiNi Guo, XiaoAi Li and Feng Qi
School of Mathematics and Informatics,
Henan Polytechnic University,
Jiaozuo City, Henan Province, 454010,
China.
bai.ni.guo@gmail.com
College of Mathematics and Information Science,
Henan Normal University, Xinxiang City,
Henan Province, 453007,
China.
lxa.hnsd@163.com
Research Institute of Mathematical Inequality Theory,
Henan Polytechnic University, Jiaozuo City,
Henan Province, 454010,
China
qifeng618@gmail.com
qifeng618@hotmail.com
qifeng618@qq.com
URLhttp://rgmia.vu.edu.au/qi.html
Abstract:
The function
is logarithmically completely monotonic in (0,∞) if and only if c≥1
and its reciprocal is logarithmically completely monotonic in (0,∞) if and only if
c≤0. The function
is completely monotonic in (0,∞) if and only if c≥1 and its
negative is completely monotonic in (0,∞) if and only if c≤0.
Paper's Title:
An Approximation of Jordan Decomposable Functions for a Lipschitz Function
Author(s):
Ibraheem Alolyan
Mathematics Department,
College of Science, King Saud University
P.O.Box: 2455, Riyadh 11451,
Saudi Arabia
ialolyan05@yahoo.com
Abstract:
The well known Jordan decomposition theorem gives the useful characterization that any function of bounded variation can be written as the difference of two increasing functions. Functions which can be expressed in this way can be used to formulate an exclusion test for the recent Cellular Exclusion Algorithms for numerically computing all zero points or the global minima of functions in a given cellular domain [2,8,9]. In this paper we give an algorithm to approximate such increasing functions when only the values of the function of bounded variation can be computed. For this purpose, we are led to introduce the idea of εincreasing functions. It is shown that for any Lipschitz continuous function, we can find two εincreasing functions such that the Lipschitz function can be written as the difference of these functions.
Paper's Title:
On Some Remarkable Product of Thetafunction
Author(s):
M. S. Mahadeva Naika, M. C. Maheshkumar and K. Sushan Bairy
Department of Mathematics,
Bangalore University, Central College Campus,
Bangalore560 001,
INDIA
msmnaika@rediffmail.com
softmahe@rediffmail.com
ksbairy@gmail.com
Abstract:
On pages 338 and 339 in his first notebook, Ramanujan records eighteen values for a certain product of thetafunction. All these have been proved by B. C. Berndt, H. H. Chan and LC. Zhang [4]. Recently M. S. Mahadeva Naika and B. N. Dharmendra [7, 8] and Mahadeva Naika and M. C. Maheshkumar [9] have obtained general theorems to establish explicit evaluations of Ramanujan's remarkable product of thetafunction. Following Ramanujan we define a new function b_{M,N} as defined in (1.5). The main purpose of this paper is to establish some new general theorems for explicit evaluations of product of thetafunction.
Paper's Title:
Equilibria and Periodic Solutions of Projected Dynamical Systems on Sets with Corners
Author(s):
Matthew D. Johnston and MonicaGabriela Cojocaru
Department of Applied Mathematics, University of Waterloo,
Ontario, Canada
mdjohnst@math.uwaterloo.ca
Department of Mathematics & Statistics, University of
Guelph,
Ontario, Canada
mcojocar@uoguelph.ca
Abstract:
Projected dynamical systems theory represents a bridge between the static worlds of variational inequalities and equilibrium problems, and the dynamic world of ordinary differential equations. A projected dynamical system (PDS) is given by the flow of a projected differential equation, an ordinary differential equation whose trajectories are restricted to a constraint set K. Projected differential equations are defined by discontinuous vector fields and so standard differential equations theory cannot apply. The formal study of PDS began in the 90's, although some results existed in the literature since the 70's. In this paper we present a novel result regarding existence of equilibria and periodic cycles of a finite dimensional PDS on constraint sets K, whose points satisfy a corner condition. The novelty is due to proving existence of boundary equilibria without using a variational inequality approach or monotonicity type conditions.
Paper's Title:
The εSmall Ball Drop Property
Author(s):
C. Donnini and A. Martellotti
Dipartimento
di Statistica e Matematica per la Ricerca Economica,
Università degli Studi di Napoli "Parthenope",
Via Medina, 80133 Napoli,
Italy
chiara.donnini@uniarthenope.it
{Dipartimento di Matematica e Informatica,
Università degli Studi di Perugia,
Via Pascoli  06123 Perugia,
Italy.
amart@dipmat.unipg.it
URL:
www.dipmat.unipg.it/~amart/
Abstract:
We continue the investigation on classes of small sets in a Banach space that give alternative formulations of the Drop Property. The small sets here considered are the set having the small ball property, and we show that for sets having nonempty 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.
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@univperp.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 elasticviscoplastic 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.
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 DharMahraz
B.P 1796 Atlas Fés,
Maroc.
rhoudaf_mohamed@yahoo.fr
Abstract:
In this paper , we study the existence of a weak solutions for the initialboundary value problems of the strongly nonlinear degenerated parabolic equation,
∂u  +A(u)+g(x,t,u,∇ u)=f 
∂t 
where A is a Leraylions operator acted from L^{p}(0,T,W_{0}^{1,p}(Ώ,w)) into its dual. g(x,t,u,∇ u) is a nonlinear term with critical growth condition with respect to ∇ u and no growth with respect to u. The source term f is assumed to belong to L^{p'}(0,T,W^{1,p'}(Ώ,w^{*})).
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 twostep 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.
Paper's Title:
Linearly Transformable Minimal Surfaces
Author(s):
Harold R. Parks and Walter B. Woods
Department of Mathematics,
Oregon State University,
Corvallis, Oregon 973314605,
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 R^{3} 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.
Paper's Title:
On the Convergence in Law of Iterates of RandomValued Functions
Author(s):
Karol Baron
Uniwersytet
Śląski,
Instytut Matematyki
Bankowa 14,
PL40007 Katowice,
Poland
baron@us.edu.pl
Abstract:
Given a probability space (Ω, A, P) a separable and complete metric space X with the σalgebra B of all its Borel subsets and a B A measurable f : X * Ω → X we consider its iterates f^{n}, n N, defined on X * Ω^{N} by f^{1}(x,ω) = f(x,ω_{1}) and f^{n+1}(x,ω)=f(f^{n}(x,ω),ω_{n+1}), provide a simple criterion for the convergence in law of f^{n}(x,·))_{ n N}, to a random variable independent of x X , and apply this criterion to linear functional equations in a single variable.
Paper's Title:
Ulam Stability of Functional Equations
Author(s):
Stefan Czerwik and Krzysztof Król
Institute of Mathematics
Silesian University of Technology
Kaszubska 23,
44100 Gliwice,
Poland
Stefan.Czerwik@polsl.pl
Krzysztof.Krol@polsl.pl
Abstract:
In this survey paper we present some of the main results on UlamHyersRassias stability for important functional equations.
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.
Paper's Title:
Stability of Almost Multiplicative Functionals
Author(s):
Norio Niwa, Hirokazu Oka, Takeshi Miura and SinEi Takahasi
Faculty of Engineering, Osaka ElectroCommunication University,
Neyagawa 5728530,
Japan
Faculty of Engineering, Ibaraki University,
Hitachi 3168511,
Japan
Department of Applied Mathematics and Physics, Graduate School of
Science and Engineering,
Yamagata University,
Yonezawa 9928510
Japan
oka@mx.ibaraki.ac.jp
miura@yz.yamagatau.ac.jp
sinei@emperor.yz.yamagatau.ac.jp
Abstract:
Let δ and p be nonnegative real numbers. Let be the real or complex number field and a normed algebra over . If a mapping satisfies
then we show that φ is multiplicative or for all If, in addition, φ satisfies
for some p≠1, then by using HyersUlamRassias 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.
Paper's Title:
Some Open Problems in Analysis
Author(s):
A.G. Ramm
Mathematics Department, Kansas State University,
Manhattan, KS 665062602,
USA
ramm@math.ksu.edu
URL: http://www.math.ksu.edu/~ramm
Abstract:
In this paper some open problems in analysis are formulated. These problems were formulated and discussed by the author at ICMAA6.
Paper's Title:
HyersUlamRassias Stability of a Generalized Jensen Functional Equation
Author(s):
A. Charifi, B. Bouikhalene, E. Elqorachi and A. Redouani
Department of
Mathematics, Faculty of Sciences,
Ibn Tofail University,
Kenitra, Morocco
charifi2000@yahoo.fr
bbouikhalene@yahoo.fr
Department of
Mathematics, Faculty of Sciences,
Ibn Zohr University,
Agadir, Morocco
elqorachi@hotmail.com
Redouaniahmed@yahoo.fr
Abstract:
In this paper we obtain the HyersUlamRassias stability for the generalized Jensen's functional equation in abelian group (G,+). Furthermore we discuss the case where G is amenable and we give a note on the HyersUlamstability of the Kspherical (n × n)matrix functional equation.
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.
Paper's Title:
On some Strongly Nonlinear Elliptic Problems in L¹data 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
DharMahraz,
B.P 1796 Atlas Fès,
Maroc
Departement of Mathematics,
Faculty of Sciences and Techniques of Tangier,
B.P. 416, Tangier,
Morocco.
rhoudaf_mohamed@yahoo.fr
Abstract:
This paper is concerned with the existence result of the
unilateral problem associated to the equations of the type
in Orlicz spaces, without
assuming the sign condition in the nonlinearity g. The source term f belongs to L¹(Ώ).
Paper's Title:
On the Fock Representation of the Central Extensions of the Heisenberg Algebra
Author(s):
L. Accardi and A. Boukas
Centro Vito Volterra, Università di Roma
Tor Vergata,
via Columbia 2, 00133 Roma,
Italy
accardi@volterra.mat.uniroma2.it
URL: http://volterra.mat.uniroma2.it
Department of Mathematics,
American College of Greece,
Aghia Paraskevi, Athens 15342,
Greece
andreasboukas@acg.edu
Abstract:
We examine the possibility of a direct Fock representation of the recently obtained nontrivial central extensions of the Heisenberg algebra, generated by elements and E satisfying the commutation relations , and , where a and are dual, h is selfadjoint, E is the nonzero selfadjoint 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 selfadjoint operator
Paper's Title:
On the product of Mmeasures in lgroups
Author(s):
A. Boccuto, B. Riěcan, and A. R. Sambucini
Dipartimento di Matematica e Informatica,
via Vanvitelli, 1 I06123 Perugia,
Italy.
boccuto@dipmat.unipg.it
URL:
http://www.dipmat.unipg.it/~boccuto
Katedra Matematiky, Fakulta Prírodných Vied,
Univerzita Mateja Bela,
Tajovského, 40, Sk97401 Banská Bystrica,
Slovakia.
riecan@fpv.umb.sk
Dipartimento di Matematica e Informatica,
via Vanvitelli, 1 I06123 Perugia,
Italy.
matears1@unipg.it
URL:
http://www.unipg.it/~matears1
Abstract:
Some extensiontype theorems and compactness
properties for the
product of lgroupvalued Mmeasures are proved.
Paper's Title:
Fractional Integral Operators and Olsen Inequalities on NonHomogeneous Spaces
Author(s):
Idha Sihwaningrum, Herry P. Suryawan, Hendra Gunawan
Analysis and Geometry Group,
Faculty of Mathematics and Natural Sciences,
Bandung Institute of Technology, Bandung 40132,
Indonesia
hgunawan@math.itb.ac.id
URL:
http://personal.fmipa.itb.ac.id/hgunawan/
Abstract:
We prove the boundedness of the fractional integral operator I_{α} on generalized Morrey spaces of nonhomogeneous type. In addition, we also present Olsentype inequalities for a multiplication operator involving I_{α}. Our proof uses a result of GarcíaCuerva and Martell [3].
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 UniversityChennai,
Saram604 703,
India.
sivasaisastha@rediffmail.com
School of Sciences and Humanities,
VIT University, Vellore632 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.
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 BrudnyiKrugljak associated with the quasipower 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 noncommutative symmetric spaces of measurable operators affiliated with a semifinite von Neumann algebra.
Paper's Title:
Two Remarks on Commutators of Hardy Operator
Author(s):
Yasuo KomoriFuruya
School of High Technology for Human Welfare
Tokai University
317 Nishino Numazu, Shizuoka 4100395 Japan
komori@wing.ncc.utokai.ac.jp
Abstract:
Fu and Lu showed that
the commutator of multiplication operator by b and
the ndimensional Hardy operator
is bounded on L^{p} if b is in some CMO space.
We shall prove the converse of this theorem
and also prove that their result is optimal by giving a counterexample
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
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.
Paper's Title:
The Square Number by the Approximation
Author(s):
Masaki Hisasue
Asahikawa Fuji Girls' High School
Asahikawa Hanasakicho 63899
Hokkaido, Japan
masaki@fuji.ed.jp
Abstract:
In this paper, we give square numbers by using the solutions of Pell's equation.
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.
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.
Paper's Title:
On the Inequality with PowerExponential 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.
Paper's Title:
Approximation of an AQCQFunctional Equation and its Applications
Author(s):
Choonkil Park and Jung Rye Lee
Department of Mathematics,
Research Institute for Natural Sciences,
Hanyang University, Seoul 133791,
Korea;
Department of Mathematics,
Daejin University,
Kyeonggi 487711,
Korea
baak@hanyang.ac.kr
jrlee@daejin.ac.kr
Abstract:
This paper is a survey on the generalized HyersUlam stability of an AQCQfunctional equation in several spaces. Its content is divided into the following sections:
1. Introduction and preliminaries.
2. Generalized HyersUlam stability of an AQCQfunctional equation in Banach spaces: direct method.
3. Generalized HyersUlam stability of an AQCQfunctional equation in Banach spaces: fixed point method.
4. Generalized HyersUlam stability of an AQCQfunctional equation in random Banach spaces: direct method.
5. Generalized HyersUlam stability of an AQCQfunctional equation in random Banach spaces: fixed point method.
6. Generalized HyersUlam stability of an AQCQfunctional equation in nonArchimedean Banach spaces: direct method.
7. Generalized HyersUlam stability of an AQCQfunctional equation in nonArchimedean Banach spaces: fixed point method.
Paper's Title:
ANormal 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 Anormal operators in semiHilbertian 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].
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,
F67 084 Strasbourg Cedex,
France
raphaele.supper@math.unistra.fr
Abstract:
The purpose of this paper is to link information on the application u→gu with some growth conditions on the functions u and g subharmonic in the unit ball of R^{N}. Two kinds of growth are considered: the Blochtype growth and growth conditions expressed through integrals involving involutions of the unit ball.
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@upgploiesti.ro.
High School Affiliated to Wuhan University, China
Abstract:
In this paper, we give two sets of necessary and sufficient conditions that the inequality f_{4}(x,y,z) ≥ 0 holds for any real numbers x,y,z, where f_{4}(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 f_{4}(1,1,1)=0, we get the main result in [3]. Several applications are given to show the effectiveness of the proposed methods.
Paper's Title:
Parachaotic Tuples of Operators
Author(s):
Bahmann Yousefi and Javad Izadi
Department of Mathematics,
Payame Noor University,
P.O. Box 193953697, Tehran,
Iran
b_yousefi@pnu.ac.ir
javadie2003@yahoo.com
Abstract:
In this paper, we introduce parachaotic tuples of operators and we give some relations between parachaoticity and Hypercyclicity Criterion for a tuple of operators.
Paper's Title:
Solution of Inequalities with PowerExponential Functions by Cîrtoaje
Author(s):
Masaki Hisasue
Asahikawa fuji girls' high school,
Asahikawa Hanasakicho 63899, Hokkaido,
Japan
Abstract:
In this paper, we prove the open inequality a^{2b}+b^^{2a} < 1 for all nonnegative real numbers a and b such that a+b=1.
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,
44280Malatya,
Turkey
Abstract:
The sufficient conditions for y_{1}(x)≤ y_{2}(x) were given in [1] such that y_{m}(x)=f_{m}(x)+∫_{a}^{x} K_{m}(x, t)y_{m}(t)dt,(m=1,2) and x∈ [a, b]. Some properties such as positivity, boundedness and monotonicity of the solution of the linear Volterra integral equation of the form f(t)=1∫_{0}^{t}K(tτ)f(τ)dτ=1K*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)=1K* f and n≥ 2, it is derived that there exist the functions L_{2}, L_{3},..., L_{n} which can be obtained by means of K and some inequalities among the functions f, h_{2}, h_{3},..., h_{i} for i=2, 3,...., n are satisfied on the infinite interval [0, ∞), where h_{i} is the solution of the equation h_{i}(t)=1L_{i}* h_{i} and n is a natural number.
Paper's Title:
On Convergence Theorems of an Implicit Iterative Process with Errors for a Finite Family of Asymptotically quasi Inonexpansive 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
Abstract:
In this paper we prove the weak and strong convergence of the implicit iterative process with errors to a common fixed point of a finite family {T_{j}}^{N}_{i=1} of asymptotically quasi I_{j}nonexpansive mappings as well as a family of {Ij}^{N}_{j=1} of asymptotically quasi nonexpansive mappings in the framework of Banach spaces. The obtained results improve and generalize the corresponding results in the existing literature.
Paper's Title:
A Geometric Generalization of BusemannPetty 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 BusemannPetty problem. In 2003, Giannapoulos [1] defined a norm for a new class of halfsection. Based on this norm, we give a geometric generalization of BusemannPetty problem, and get its answer as a result
Paper's Title:
C^{*}algebras Associated Noncommutative Circle and Their Ktheory
Author(s):
Saleh Omran
Taif University,
Faculty of Science,
Taif,
KSA
South Valley University,
Faculty of Science,
Math. Dep.
Qena,
Egypt
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 S_{1}^{nc}. We examine the Ktheory of this algebra and the subalgebras S_{1}^{nc}/I_{k}, I_{k} . Where I_{k}, for each k, is the ideal in S_{1}^{nc} generated by all products of generators h_{s} containing at least k+1 pairwise different generators. Moreover we prove that such algebra divided by the ideal I_{2} is commutative.
Paper's Title:
Numerical Solution of A System of Singularly Perturbed ConvectionDiffusion BoundaryValue 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 convectiondiffusion 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 firstorder 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.
Paper's Title:
An Improvement of the HermiteHadamard Inequality for Functions Convex on the Coordinates
Author(s):
Milica Klaričić Bakula
Faculty of Science,
University of Split,
Teslina 12, 21000 Split.
Croatia
Email: milica@pmfst.hr
Abstract:
An improvement of the HermiteHadamard inequality for functions convex on the coordinates is given.
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.
Email:
tabataba@math.susc.ac.ir
zebarjad@mail.yu.ac.ir
URL:
http://research.shirazu.ac.ir/faculty/More.asp?ID=207
Abstract:
By a partial dynamical system, we mean a triple containing a C*algebra A, a discrete group G and a partial action of G on A. There are two C*algebras associated to a given partial dynamical system. These are nothing but the certain C*completions of a Banach *algebra. In constructing such a Banach *algebra, usually, a tedious limit process is used to apply. In this paper, we prove some theorems in this context without any limit process.
Paper's Title:
L∞ Error Estimate of Schwarz Algorithm for Elliptic QuasiVariational Inequalities Related to Impulse Control Problem
Author(s):
Saadi Samira and Mehri Allaoua
Lab. LANOS, Department of Mathematics,
University Badji Mokhtar Annaba,
P.O.Box 12, Annaba 23000,
Algeria.
Lab. LAIG, Department of Mathematics,
University May 8th 1945,
P.O.Box 401, Guelma 24000,
Algeria.
Email:
saadisamira69@yahoo.fr
allmehri@yahoo.fr
Abstract:
In this work, we study Schwarz method for a class of elliptic quasivariational 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.
Paper's Title:
Application of Equivalence Method to Classify MongeAmpère Equations of Elliptic Type
Author(s):
Moheddine Imsatfia
Email: imsatfia@math.jussieu.fr
Abstract:
In this paper, we apply Cartan's equivalence method to give a local classification of MongeAmpère equations of elliptic type. Then we find a necessary and sufficient conditions such that a MongeAmpère equation is either contactomorphic to the Laplace equation or to an EulerLagrange equation.
Paper's Title:
Scope of the Logarithmic Mean
Author(s):
Murali Rao and Agnish Dey
Department of Mathematics,
University of Florida,
1400 Stadium Road, Gainesville,
Florida 32611,
U. S. A.
Email: mrao@ufl.edu
URL: http://people.clas.ufl.edu/mrao
Email: 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.
Paper's Title:
A_{p} Functions and Maximal Operator
Author(s):
Chunping Xie
Department of Mathematics,
Milwaukee School of Engineering,
1025 N. Broadway,
Milwaukee, Wisconsin 53202,
U. S. A.
Email: xie@msoe.edu
URL: http://www.msoe.edu/people/chunping.xie
Abstract:
The relationship between A_{p} functions and HardyLittlewood maximal operator on L^{p,λ}(w), the weighted Morrey space, has been studied. Also the extropolation theorem of L^{p,λ}(w) has been considered.
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 366880002,
USA.
Email:
prokhoro@southalabama.edu
URL:
http://www.southalabama.edu/mathstat/people/prokhorov.shtml
Abstract:
We study a constructive method of rational approximation of analytic functions based on ideas of the theory of Hankel operators. Some properties of the corresponding Hankel operator are investigated. We also consider questions related to the convergence of rational approximants. Analogues of Montessus de Ballore's and Gonchars's theorems on the convergence of rows of Padé approximants are proved.
Paper's Title:
Examples of Fractals Satisfying the Quasihyperbolic Boundary Condition
Author(s):
Petteri Harjulehto and Riku Klén
Department of Mathematics and Statistics,
FI20014 University of Turku,
Finland
Email: petteri.harjulehto@utu.fi
Email: 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.
Paper's Title:
Some Grüss Type Inequalities in Inner Product Spaces
Author(s):
Sever S. Dragomir^{1,2}
^{1}Mathematics, School of Engineering
& Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
Email: sever.dragomir@vu.edu.au
^{2}School 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.
Paper's Title:
Weak Type Inequalities for Some Operators on Generalized Morrey Spaces Over Metric Measure Spaces
Author(s):
Idha Sihwaningrum, Ari Wardayani, Hendra Gunawan
Faculty of Mathematics and Natural
Sciences,
Jenderal Soedirman University, Purwokerto 53122,
Indonesia.
Email: idha.sihwaningrum@unsoed.ac.id
ariwardayani@yahoo.co.id
Faculty of Mathematics and Natural
Sciences,
Bandung Institute of Technology, Bandung 40132,
Indonesia.
Email: hgunawan@math.itb.ac.id
URL:
http://personal.fmipa.itb.ac.id/hgunawan/
Abstract:
We discuss weak type inequalities for maximal and fractional integral operators on generalized Morrey spaces over metric measure spaces. Here the measure satisfies the so called growth condition. By taking into account the maximal operator, we obtain a Hedberg type inequality, which leads us to the weak type inequality for the fractional integral operator on the same spaces.
Paper's Title:
On the HyersUlam Stability of Homomorphisms and Lie Derivations
Author(s):
Javad Izadi and Bahmann Yousefi
Department of Mathematics, Payame Noor
University,
P.O. Box: 193953697, Tehran,
Iran.
Email: javadie2003@yahoo.com,
b_yousefi@pnu.ac.ir
Abstract:
Let A be a Lie Banach^{*}algebra. For each elements (a, b) and (c, d) in A^{2}:= A * A, by definitions
(a, b) (c, d)= (ac, bd),
(a, b)= a+ b,
(a, b)^{*}= (a^{*}, b^{*}),
A^{2} 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: A^{2}→A^{2} 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 A^{2}. Furthermore, if A is a Lie Banach^{*}algebra, then D is called a Lie^{*} derivation on A^{2} whenever D is a Lie derivation with D (a, b)^{*}= D (a^{*}, b^{*}) for all a, b∈A. In this paper, we investigate the HyersUlam stability of Lie Banach^{*}algebra homomorphisms and Lie^{* }derivations on the Banach^{*}algebra A^{2}.
Paper's Title:
On the Constant in a Transference Inequality for the Vectorvalued 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/
Email:
J.M.A.M.vanNeerven@TUDelft.nl
Email: D.C.Gijswijt@TUDelft.nl
Abstract:
The standard proof of the equivalence of Fourier type on R^{d} and on the torus T^{d} is usually stated in terms of an implicit constant, defined as the minimum of a sum of powers of sinc functions. In this note we compute this minimum explicitly.
Paper's Title:
Hyponormal and KQuasiHyponormal Operators On SemiHilbertian Spaces
Author(s):
Ould Ahmed Mahmoud Sid Ahmed and Abdelkader Benali
Mathematics Department,
College of Science,
Aljouf University,
Aljouf 2014,
Saudi Arabia.
Email:
sididahmed@ju.edu.sa
Mathematics Department, Faculty of
Science,
Hassiba Benbouali, University of Chlef,
B.P. 151 Hay Essalem, Chlef 02000,
Algeria.
Email:
benali4848@gmail.com
Abstract:
Let H be a Hilbert space and let A be a positive bounded operator on H. The semiinner product < uv>_{A}:=<Auv>, u,v ∈ H induces a seminorm  ._{A} on H. This makes H into a semiHilbertian space. In this paper we introduce the notions of hyponormalities and kquasihyponormalities 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 quasihyponormal operators. An operator T ∈ B_{A} (H) is said to be (A, k)quasihyponormal if
Paper's Title:
The boundedness of BesselRiesz operators on generalized Morrey spaces
Author(s):
Mochammad Idris, Hendra Gunawan and Eridani
Department of Mathematics,
Bandung Institute of Technology,
Bandung 40132,
Indonesia.
Email:
mochidris@students.itb.ac.id
Department of Mathematics,
Bandung Institute of Technology,
Bandung 40132,
Indonesia.
Email: hgunawan@math.itb.ac.id
URL:
http://personal.fmipa.itb.ac.id/hgunawan/
Department of Mathematics,
Airlangga University,
Surabaya 60115,
Indonesia.
Email: eridani.dinadewi@gmail.com
Abstract:
In this paper, we prove the boundedness of BesselRiesz operators on generalized Morrey spaces. The proof uses the usual dyadic decomposition, a Hedbergtype inequality for the operators, and the boundedness of HardyLittlewood maximal operator. Our results reveal that the norm of the operators is dominated by the norm of the kernels.
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.
Email:
Yari@iust.ac.ir
Email:
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
Qarzolhasaneh
Mehr Iran Bank, Tehran,
Iran.
Email:
B.moomivand@qmb.ir
Department of Mathematics and Statistics,
University of Northern British Columbia,
Prince George, BC,
Canada.
Email:
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.
Paper's Title:
Stability of an Almost Surjective epsilonIsometry 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.
Email:
miminanira@gmail.com
Department of Mathematics, Faculty of
Mathematics and Natural Sciences,
Brawijaya University,
Jl. Veteran Malang 65145,
Indonesia.
Email:
rbagus@ub.ac.id
Department of Mathematics, Faculty of
Mathematics and Natural Sciences,
Brawijaya University,
Jl. Veteran Malang 65145,
Indonesia.
Email:
marjono@ub.ac.id
Abstract:
In this paper, we study the stability of epsilonisometry in the dual of real Banach spaces. We prove that the almost surjective epsilonisometry mapping is stable in dual of each spaces. The proof uses Gâteaux differentiability space (GDS), weakstar exposed points, normattaining operator, and some studies about epsilonisometry that have been done before.
Paper's Title:
Robust Error Analysis of Solutions to Nonlinear Volterra Integral Equation in L^{p} Spaces
Author(s):
Hamid Baghani, Javad FarokhiOstad and Omid Baghani
Department of Mathematics, Faculty of
Mathematics,
University of Sistan and Baluchestan, P.O. Box 98135674, Zahedan,
Iran.
Email:
h.baghani@gmail.com
Department of Mathematics, Faculty of
Basic Sciences,
Birjand University of Technology, Birjand,
Iran.
Email: j.farrokhi@birjandut.ac.ir
Department of Mathematics and Computer
Sciences,
Hakim Sabzevari University, P.O. Box 397, Sabzevar,
Iran.
Email:
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.
Paper's Title:
Strong Convergence Theorem for a Common Fixed Point of an Infinite Family of Jnonexpansive Maps with Applications
Author(s):
Charlse Ejike Chidume, Otubo Emmanuel Ezzaka and Chinedu Godwin Ezea
African University of Science and
Technology,
Abuja,
Nigeria.
Email:
cchidume@aust.edu.ng
Ebonyi State University,
Abakaliki,
Nigeria.
Email: mrzzaka@yahoo.com
Nnamdi Azikiwe University,
Awka,
Nigeria.
Email: chinedu.ezea@gmail.com
Abstract:
Let E be a uniformly convex and uniformly smooth real Banach space with dual space E^{*}. Let {T_{i}}^{∞}_{i=1} be a family of Jnonexpansive maps, where, for each i,~T_{i} maps E to 2^{E*}. A new class of maps, Jnonexpansive maps from E to E^{*}, an analogue of nonexpansive self maps of E, is introduced. Assuming that the set of common Jfixed points of {T_{i}}^{∞}_{i=1} is nonempty, an iterative scheme is constructed and proved to converge strongly to a point x^{*} in ∩^{∞}_{n=1}F_{J}T_{i}. This result is then applied, in the case that E is a real Hilbert space to obtain a strong convergence theorem for approximation of a common fixed point for an infinite family of nonexpansive maps, assuming existences. The theorem obtained is compared with some important results in the literature. Finally, the technique of proof is also of independent interest.
Paper's Title:
Lower and Upper Bounds for the PointWise Directional Derivative of the Fenchel Duality Map
Author(s):
M. Raissouli^{1,2}, M. Ramezani^{3}
^{1}Department
of Mathematics,
Science Faculty, Taibah University,
P.O. Box 30097, Zip Code 41477, Al Madinah Al Munawwarah,
Saudi Arabia.
^{2}Department
of Mathematics,
Science Faculty, Moulay Ismail University, Meknes,
Morocco.
Email:
raissouli.mustapha@gmail.com
^{3}Department
of Mathematics,
University of Bojnord, Bojnord,
Iran.
Email: m.ramezani@ub.ac.ir
Abstract:
In this paper, we introduce the pointwise directional derivative of the Fenchel duality map and we study its properties. The best lower and upper bounds of this pointwise directional derivative are also given. We explain how our functional results contain those related to the positive bounded linear operators.
Paper's Title:
Strong Convergence Theorems for a Common Zero of an Infinite Family of GammaInverse 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.
Email: cchidume@aust.edu.ng
Email: romanusogonnaya@gmail.com
Email: nnyabavictoriau@gmail.com
Abstract:
Let E be a uniformly convex and uniformly smooth real Banach space with
dual space E^{*} and let A_{k}:E→E^{*},
k=1, 2, 3 , ...
be a family of inverse strongly monotone maps such that ∩^{∞}_{k=1}
A_{k}^{1}(0)≠∅.
A new iterative algorithm is constructed and proved to converge strongly to a
common zero of the family.
As a consequence of this result, a strong convergence theorem for approximating
a common Jfixed point for an infinite family of
gammastrictly Jpseudocontractive maps is proved. These results are new and
improve recent results obtained for these classes of nonlinear maps.
Furthermore, the technique of proof is of independent interest.
Paper's Title:
Applications of the Structure Theorem of (w_{1},w_{2})Tempered Ultradistributions
Author(s):
Hamed M. Obiedat and Lloyd E. Moyo
Department of Mathematics,
Hashemite University,
P.O.Box 150459, Zarqa13115,
Jordan.
Email: hobiedat@hu.edu.j
Department of Mathematics, Computer
Science & Statistics,
Henderson State University,
1100 Henderson Street, Arkadelphia, AR 71999,
USA.
Email: moyol@hsu.edu
Abstract:
Using a previously obtained structure theorem for (w_{1}, w_{2})tempered ultradistributions, we prove that these ultradistributions can be represented as initial values of solutions of the heat equation.
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 Delhi110007,
India.
Email: rajkmc@gmail.com
Department of Mathematics,
University of Delhi,
New Delhi110007,
India
Email: manish17102021@gmail.com
Department of Mathematics,
Hans Raj College, University of Delhi,
New Delhi110007,
India
Email: reena.bhagwat29@gmail.com
Abstract:
In this paper, we present sufficient condition for the sequence of vectors to be a frame for H^{s}(R^{d}) are derived. Necessary and sufficient conditions for the sequence of vectors to be tight wavelet frames in H^{s}(R^{d}) are obtained. Further, as an application an example of tight wavelet frames for H^{s}(R^{2}) as bivariate box spline over 3direction are given.
Paper's Title:
Weakly Compact Composition Operators on Real Lipschitz Spaces of Complexvalued Functions on Compact Metric Spaces with Lipschitz Involutions
Author(s):
D. Alimohammadi and H. Alihoseini
Department of Mathematics,
Faculty of Science,
Arak University
P. O. Box,3815688349,
Arak,
Iran.
Email: dalimohammadi@araku.ac.ir
Email:
hr_alihoseini@yahoo.com
URL: http://www.araku.ac.ir
Abstract:
We first show that a bounded linear operator T on a real Banach space E is weakly compact if and only if the complex linear operator T on the complex Banach space E_{C} is weakly compact, where E_{C} is a suitable complexification of E and iT' is the complex linear operator on E_{C} associated with T. Next we show that every weakly compact composition operator on real Lipschitz spaces of complexvalued functions on compact metric spaces with Lipschitz involutions is compact.
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.
Email: mostefanadir@yahoo.fr
Email: 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.
Paper's Title:
BirkhoffJames orthogonality and Best Approximant in L_{1}(X)
Author(s):
Mecheri Hacene and Rebiai Belgacem
Department of Mathematics and
Informatics,
LAMIS laboratory, University of Tebessa,
Algeria.
Email: mecherih2000@yahoo.fr
Department of Mathematics and
Informatics,
LAMIS laboratory, University of Tebessa,
Algeria.
Email: brebiai@gmail.com
Abstract:
Let X be a complex Banach space and let (X,ρ) be a positive measure space. The BirkhoffJames orthogonality is a generalization of Hilbert space orthogonality to Banach spaces. We use this notion of orthogonality to establish a new characterization of BirkhoffJames orthogonality of bounded linear operators in L_{1}(X,ρ) also implies best approximation has been proved.
Paper's Title:
Generalized kdistancebalanced Graphs
Author(s):
Amir Hosseini and Mehdi Alaeiyan
Department of mathematics, Karaj Branch,
Islamic Azad university, Karaj,
Iran.
Email: amir.hosseini@kiau.ac.ir,
hosseini.sam.52@gmail.com
Department of Mathematics,
Iran University of Science and Technology, Tehran,
Iran.
Email: alaeiyan@iust.ac.ir
Abstract:
A nonempty graph Γ is called generalized kdistancebalanced, 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.
Paper's Title:
Invariant Subspaces Close to Almost Invariant Subspaces for Bounded Linear Operators
Author(s):
M. A. Farzaneh, A. Assadi and H. M. Mohammadinejad
Department of Mathematical and
Statistical Sciences,
University of Birjand,
PO Box 97175/615, Birjand,
Iran.
Email: farzaneh@birjand.ac.ir
Department of Mathematical and
Statistical Sciences,
University of Birjand,
PO Box 97175/615, Birjand,
Iran.
Email: assadiaman@birjand.ac.ir
Department of Mathematical and
Statistical Sciences,
University of Birjand,
PO Box 97175/615, Birjand,
Iran.
Email: hmohammadin@birjand.ac.ir
Abstract:
In this paper, we consider some features of almost invariant subspace notion. At first, we restate the notion of almost invariant subspace and obtain some results. Then we try to achieve an invariant subspace completely close to an almost invariant subspace. Also, we introduce the notion of "almost equivalent subspaces" to simply the subject related to almost invariant subspaces and apply it.
Paper's Title:
Existence of Optimal Parameters for Damped SineGordon 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.
Email: nthapa@cameron.edu
URL: http://www.cameron.edu/~nthapa/
Abstract:
The parameter identification problem for sineGordon equation is of a major interests among mathematicians and scientists.\ In this work we the consider sineGordon equation with variable diffusion coefficient and Neumann boundary data. We show the existence and uniqueness of weak solution for sineGordon equation. Then we show that the weak solution continuously depends on parameters. Finally we show the existence of optimal set of parameters.
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
Email: bukzhalev@mail.ru
Russian Institute for Scientific and
Technical Information of the Russian Academy of Sciences,
20 Usievicha St., Moscow, 125190,
Russia
Email: 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.
Paper's Title:
A Multivalued Version of the RadonNikodym Theorem, via the Singlevalued Gould Integral
Author(s):
Domenico Candeloro^{1}, Anca Croitoru^{2}, Alina Gavriluţ^{2}, Anna Rita Sambucini^{1}
^{1}Dept. of Mathematics and Computer
Sciences,
University of Perugia,
1, Via Vanvitelli  06123, Perugia,
Italy.
Email: domenico.candeloro@unipg.it,
anna.sambucini@unipg.it
^{2}Faculty of Mathematics,
Al. I. Cuza University,
700506 Iaşi,
Romania.
Email: 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 RadonNikodym theorem relative to a fuzzy multisubmeasure which is new also in the finite dimensional case. Some results concerning the Gould integral are also obtained.
Paper's Title:
Relations Between Differentiability And Onesided Differentiability
Author(s):
Q. D. Gjonbalaj, V. R. Hamiti and L. Gjoka
Department of Mathematics, Faculty of
Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000, Kosova.
Email: qefsere.gjonbalaj@unipr.edu
{Department of Mathematics, Faculty of
Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000, Kosova.
Email: valdete.rexhebeqaj@unipr.edu
Department of Mathematical Engineering,
Polytechnic University of Tirana, Tirana,
Albania
Email: luigjgjoka@ymail.com
Abstract:
In this paper, we attempt to approach to the problem of connection between differentiation and oneside differentiation in a more simple and explicit way than in existing math literature. By replacing the condition of differentiation with onesided differentiation, more precisely with righthand differentiation, we give the generalization of a theorem having to do with Lebesgue’s integration of derivative of a function. Next, based on this generalized result it is proven that if a continuous function has bounded righthand derivative, then this function is almost everywhere differentiable, which implies that the set of points where the function is not differentiable has measure zero.
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.
Email: 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 (R_{0}). The result shows that the epidemic model has two equilibrium points. They are disease free equilibrium, [E_{0}=[S,I,R]=[1,0,0]], and epidemic equilibrium, E_{i}=[S,I,R]= [5,497808;3,680341;0,818288]. The Basic Reproduction Ratio of malaria disease in Ambon city is 0,181891. This result implies that malaria disease in Ambon will not be an endemic, because malaria disease in Ambon city will be eradicated slowly over time.
Paper's Title:
A New Interpretation of the Number e
Author(s):
Olivier de La Grandville
Faculty of Economics, Goethe University,
Frankfurt, TheodorAdorno Platz 4,
60323 Frankfurt am Main,
Germany.
Email:
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.
Paper's Title:
Action of Differential Operators On Chirpsconstruct On L^{∞}
Author(s):
Taoufik El Bouayachi and Naji Yebari
Laboratoire de Mathematiques et
applications,
Faculty of sciences and techniques, Tangier,
Morocco.
Email:
figo407@gmail.com,
yebarinaji@gmail.com
Abstract:
We will study in this work the action of differential operators on L∞ chirps and we will give a new definition of logarithmic chirp. Finally we will study the action of singular integral operators on chirps by wavelet characterization and Kernel method.
Paper's Title:
A New Adomian Approach to Solving Integral Equations of Fredholm and Volterra Second Kind
Author(s):
Ouedraogo Seny, Nebie Abdoul Wassiha, Youssouf Pare, Blaise Some
Departement de mathematiques,
Universite Joseph KiZerbo,
Burkina Faso.
Email: oseny@yahoo.fr,
nebwass@yahoo.fr
pareyoussouf@yahoo.fr,
some@univouaga.bf
Abstract:
In order to simplify the resolution of Fredholm and Volterra's second type integral equations, we propose a new approach based on the Adomian Decompositional Method (ADM). We test the new approach on several examples with success.
Paper's Title:
Extension of Factorization Theorems of Maurey to spositively Homogeneous Operators
Author(s):
Abdelmoumen Tiaiba
Department of Physics,
University of M'sila,
Algeria.
Email: tiaiba05@yahoo.fr
Abstract:
In the present work, we prove that the class of spositively homogeneous operators is a Banach space. As application, we give the generalization of some Maurey factorization theorems to T which is a spositively homogeneous operator from X a Banach space into L_{p}. Where we establish necessary and sufficient conditions to proof that T factors through L_{q}. After this we give extend result of dual factorization theorem to same class of operators above.
Paper's Title:
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.
Email:
saidameurmeziane@univeloued.dz
Departement of Mathematics,
El Oued University,
P.O. Box 789, 39000 El Oued,
Algeria.
Email:
hadjammartedjani@univeloued.dz
Department of Mathematics,
Kasdi Merbah University,
30000 Ouargla,
Algeria.
Email: maiza.laid@univouargla.dz
Abstract:
In this paper, we consider a mathematical model that describes the quasistatic process of contact between two thermoelectroviscoelastic 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.
Paper's Title:
Several Applications of a Local Nonconvex Youngtype Inequality
Author(s):
Loredana Ciurdariu, Sorin Lugojan
Department of Mathematics,
"Politehnica" University of Timisoara,
Pta. Victoriei, No.2, 300006Timisoara,
Romania.
Email: ltirtirau87@yahoo.com
Abstract:
A local version of the Young inequality for positive numbers is used in order to deduce some inequalities about determinants and norms for real quadratic matrices and norms of positive operators on complex Hilbert spaces.
Paper's Title:
ResidualBased A Posteriori Error Estimates For A Conforming Mixed Finite Element Discretization of the MongeAmpere Equation
Author(s):
J. Adetola, K. W. Houedanou and B. Ahounou
Institut de Mathematiques et de Sciences
Physiques (IMSP),
Universite d'AbomeyCalavi
Email: adetolajamal58@yahoo.com
Departement de Mathematiques,
Faculte des Sciences et Techniques (FAST),
Universite d'AbomeyCalavi
Email: khouedanou@yahoo.fr
Departement de Mathematiques,
Faculte des Sciences et Techniques (FAST),
Universite d'AbomeyCalavi
Email: bahounou@yahoo.fr
Abstract:
In this paper we develop a new a posteriori error analysis for the MongeAmpere equation approximated by conforming finite element method on isotropic meshes in R^{2}. 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.
Paper's Title:
Fractional exp(φ(ξ)) Expansion Method and its Application to SpaceTime 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.
Email: Alaamath81@gmail.com
URL:
https://scholar.google.com/citations?user=ccztZdsAAAAJ&hl=ar
Department of Management Information
System and Production Management,
College of Business and Economics, Qassim University,
P.O. BOX 6666, Buraidah: 51452,
Saudi Arabia.
Email: Lama2736@gmail.com
URL:
https://scholar.google.com/citations?user=OSiSh1AAAAAJ&hl=ar
Abstract:
In this paper, we mainly suggest a new method that depends on the fractional derivative proposed by Katugampola for solving nonlinear fractional partial differential equations. Using this method, we obtained numerous useful and surprising solutions for the spacetime fractional nonlinear WhithamBroerKaup equations and spacetime fractional generalized nonlinear HirotaSatsuma coupled KdV equations. The solutions obtained varied between hyperbolic, trigonometric, and rational functions, and we hope those interested in the reallife applications of the previous two equations will find this approach useful.
Paper's Title:
The Effect of Harvesting Activities on PreyPredator 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.
Email: muh.nurulhuda@fmipa.unmul.ac.id
fidiadta@fmipa.unmul.ac.id
ika.purnamasari@fmipa.unmul.ac.id
Abstract:
This paper discussed preypredator 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.
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.
Email: 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.
Paper's Title:
Inequalities of Gamma Function Appearing in Generalizing Probability Sampling Design
Author(s):
Mohammadkheer M. AlJararha And Jehad M. AlJararha
Department of Mathematics,
Yarmouk University,
Irbid 21163,
Jordan.
Email: mohammad.ja@yu.edu.jo
Department of Statistics,
Yarmouk University,
Irbid 21163,
Jordan.
Email: 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.
Paper's Title:
HermiteHadamard Type Inequalities for MNConvex Functions
Author(s):
Sever S. Dragomir^{1,2}
^{1}Mathematics,
College of Engineering
& Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
Email: sever.dragomir@vu.edu.au
^{2}DSTNRF 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 HermiteHadamard 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 MNconvex 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.
Paper's Title:
Rational Expressions of Arithmetic and Geometric Means for the Sequence n^{p}_{n ∈ N} and the Geometric Progression
Author(s):
M. Kinegawa, S. Miyamoto and Y. Nishizawa
Faculty of Education, Saitama University,
Shimookubo 255, Sakuraku, Saitamacity, Saitama,
Japan.
Email: m.kinegawa.645@ms.saitamau.ac.jp
Faculty of Education, Saitama University,
Shimookubo 255, Sakuraku, Saitamacity, Saitama,
Japan.
Email: s.miyamoto.245@ms.saitamau.ac.jp
Faculty of Education, Saitama University,
Shimookubo 255, Sakuraku, Saitamacity, Saitama,
Japan.
Email:
ynishizawa@mail.saitamau.ac.jp
Abstract:
In this paper, we consider the arithmetic and geometric means for the sequence n^{p}_{n ∈ N} and the geometric progression. We obtain the results associated with the rational expressions of the means.
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.
Email: 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.
Email: 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.
Paper's Title:
RiemannStieltjes Integrals and Some Ostrowski Type Inequalities
Author(s):
W. G. Alshanti
Department of General Studies,
Jubail University College,
KSA.
Email: 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, L_{1} 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.
Paper's Title:
Lie Group Theoretic Approach of OneDimensional BlackScholes Equation
Author(s):
P. L. Zondi and M. B. Matadi
Department of Mathematical sciences,
Faculty of Sciences & Agriculture, University of Zululand,
P Bag X1001, KwaDlangezwa 3886,
South Africa.
Email: matadim@unizulu.ac.za
zondip@unizulu.ac.za
Abstract:
This study discusses the Lie Symmetry Analysis of BlackScholes equation via a modified local oneparameter transformations. It can be argued that the transformation of the BlackScholes 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 BlackScholes equation are constructed and lead to invariant solutions.
Paper's Title:
On Trigonometric Approximation of Continuous Functions by Deferred Matrix Means
Author(s):
Xhevat Zahir Krasniqi
Faculty of Education,
University of Prishtina "Hasan Prishtina",
Avenue "Mother Theresa " no. 5, Prishtinë
10000,
Republic of Kosovo.
Email: xhevat.krasniqi@unipr.edu
URL:
https://staff.unipr.edu/profile/xhevatkrasniqi
Abstract:
In this paper, for the first time, we introduce the deferred matrix means which contain the wellknown generalized deferred Nörlund, deferred Nörlund, deferred Riesz, deferred Cesàro means introduced earlier by others, and a new class of sequences (predominantly a wider class than the class of Head Bounded Variation Sequences). In addition, using the deferred matrix means of Fourier series of a continuous function, we determine the degree of approximation of such function via its modulus of continuity and a positive mediate function.
Paper's Title:
A Caratheodory's Approximate Solutions of Stochastic Differential Equations Under the Hölder Condition
Author(s):
BoKyeong Kim and YoungHo Kim
Department of Mathematics,
Changwon National University,
Changwon, Gyeongsangnamdo 51140,
Korea.
Email: 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.
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.
Email: singhs2@unisa.ac.za
University of KwaZuluNatal,
School of Mathematics Statistics and Computer Sciences
Private Bag X54001,
Durban,
4000,
South Africa.
Email: 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.
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.
Email: 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 Jingfeng Tian, Minghu Ha, and Chao Wang.
Paper's Title:
Numerical Study of a Mathematical Model of a FreeSurface Potential Flow
Author(s):
H. Serguine, F. Guechi and A. Gasmi
Department Of Mathematics, Faculty of Science,
Ferhat Abbas Universty,
19000, Setif,
Algeria.
Email: houria.serguine@univmsila.dz
Department Of Mathematics, Faculty of Science,
Ferhat Abbas Universty,
19000, Setif,
Algeria.
Email: fairouz.chegaar@univsetif.dz
Laboratory of Pure and Applied Mathematics, Faculty of Mathematics and
Computer Science,
Mohamed Boudiaf Universty,
28000, M'sila,
Algeria.
Email: abdelkader.gasmi@univmsila.dz
Abstract:
In this work, the problem of a potential and twodimensional 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.
Paper's Title:
Some Notes on the Semiopen 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.
Email: nickytumalun@unima.ac.id
URL: https://fmipa.unima.ac.id/
Department of Mathematics
Universitas Negeri Manado
Tondano 95618
Indonesia.
Email: pheatuerah@unima.ac.id
URL: https://fmipa.unima.ac.id/
Department of Physics
Universitas Negeri Manado
Tondano 95618
Indonesia.
Email:
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 semiopen subspace of a topological space. More precisely, we prove that a nowhere dense set in the semiopen 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 semiopen 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 semiopen set and Baire space.
Paper's Title:
Higher Order Accurate Compact Schemes for Time Dependent Linear and Nonlinear ConvectionDiffusion Equations
Author(s):
S. Thomas, Gopika P.B. and S. K. Nadupuri
Department of Mathematics
National Institute of Technology Calicut
Kerala
673601
India.
Email:
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 convectiondiffusion 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 convectiondiffusion 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 RungeKutta scheme in time combined to find the numerical solution of one dimensional nonlinear convectiondiffusion 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 predictorcorrector method is proposed. A comparative study is performed of the proposed schemes with existing predictorcorrector method. The investigation of computational order of convergence is presented.
Paper's Title:
Using Direct and Fixed Point Technique of Cubic Functional Equation and its HyersUlam 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.
Email: 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 HyersUlam stability results for the above mentioned functional equation in Fuzzy Banach spaces by means of direct and fixed point methods.
Paper's Title:
A General Fractional Control Scheme for Compound Combination Synchronization Between Different FractionalOrder Identical Chaotic Systems
Author(s):
Soumia Bensimessaoud and Smail Kaouache
Laboratory of Mathematics and their interactions, Abdelhafid Boussouf University Center, Mila, Algeria.
Email:
soumiabensimessaoud@gmail.com,
smailkaouache@gmail.com
Abstract:
In this paper, we aim to investigate the problem of compound combination synchronization (CCS) between four different fractionalorder 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.
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.
Email:
spiros.konstantogiannis@ronininstitute.org
URL:
https://www.researchgate.net/profile/SpirosKonstantogiannis
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.
Paper's Title:
Eigenvalue Bounds based on Projections
Author(s):
Pravin Singh, Shivani Singh, Virath Singh
University of KwaZuluNatal,
Private Bag X54001,
Durban, 4001,
South Africa.
University of South Africa,
Department of Decision Sciences, PO Box 392,
Pretoria,0003,
South Africa.
University of KwaZuluNatal,
Private Bag X54001,
Durban, 4001,
South Africa.
Email:
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 n2 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.
Paper's Title:
Optimal Conditions using Multivalued GPresic 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.
Email: debsarkar1996@gmail.com
Department of Mathematics, Amity
University, Kadampukur, 24PGS(N), Kolkata, West Bengal, 700135,
India.
Email: drrkbhardwaj100@gmail.com
School of Engineering and Technology,
Jagran Lakecity University, Bhopal, MP462044,
India.
Email: drvandana@jlu.edu.in
Department of Mathematics,
VIT University, Chennai, Tamil Nadu600127,
India.
Email: pulakkonar@gmail.com
Abstract:
In the present paper, some best proximity results have been presented using the concept of GPresic type multivalued mapping. These results are the extensions of Presic's theorem in the nonself mapping. A suitable example has also been given. Here, some applications are presented in θchainable space and ordered metric space.
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