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The Australian Journal of Mathematical Analysis and Applications
ISSN 1449-5910 |
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Paper's Title:
Analytical and Numerical Solutions of the Inhomogenous Wave Equation
Author(s):
T. Matsuura and S. Saitoh
Department of Mechanical Engineering, Faculty of Engineering,
Gunma University, Kiryu 376-8515, Japan
matsuura@me.gunma-u.ac.jp
Department of Mathematics, Faculty of Engineering,
Gunma University, Kiryu 376-8515, Japan
ssaitoh@math.sci.gunma-u.ac.jp
Abstract:
In this paper, by a new concept and method we give approximate
solutions of the inhomogenous wave equation on multidimensional spaces.
Numerical experiments are conducted as well.
Paper's Title:
Solving Non-Autonomous Nonlinear Systems of Ordinary Differential Equations Using Multi-Stage Differential Transform Method
Author(s):
K. A. Ahmad, Z. Zainuddin, F. A. Abdullah
School of Mathematical Sciences
Universiti Sains Malaysia
11800 USM Penang
Malaysia.
E-mail: abumohmmadkh@hotmail.com
zarita@usm.my
farahaini@usm.my
Abstract:
Differential equations are basic tools to describe a wide variety of phenomena in nature such as, electrostatics, physics, chemistry, economics, etc. In this paper, a technique is developed to solve nonlinear and linear systems of ordinary differential equations based on the standard Differential Transform Method (DTM) and Multi-stage Differential Transform Method (MsDTM). Comparative numerical results that we are obtained by MsDTM and Runge-Kutta method are proposed. The numerical results showed that the MsDTM gives more accurate approximation as compared to the Runge-Kutta numerical method for the solutions of nonlinear and linear systems of ordinary differential equations
Paper's Title:
Rational Expressions of Arithmetic and Geometric Means for the Sequence
npn ∈ N and the Geometric Progression
Author(s):
M. Kinegawa, S. Miyamoto and Y. Nishizawa
Faculty of Education, Saitama University,
Shimo-okubo 255, Sakura-ku, Saitama-city, Saitama,
Japan.
E-mail: m.kinegawa.645@ms.saitama-u.ac.jp
Faculty of Education, Saitama University,
Shimo-okubo 255, Sakura-ku, Saitama-city, Saitama,
Japan.
E-mail: s.miyamoto.245@ms.saitama-u.ac.jp
Faculty of Education, Saitama University,
Shimo-okubo 255, Sakura-ku, Saitama-city, Saitama,
Japan.
E-mail:
ynishizawa@mail.saitama-u.ac.jp
Abstract:
In this paper, we consider the arithmetic and geometric means for the sequence npn ∈ N and the geometric progression. We obtain the results associated with the rational expressions of the means.
Paper's Title:
Coexisting Attractors and Bubbling Route to Chaos in Modified Coupled Duffing Oscillators
Author(s):
B. Deruni1, A. S. Hacinliyan1,2, E. Kandiran3, A. C. Keles2, S. Kaouache4, M.-S. Abdelouahab4, N.-E. Hamri4
1Department
of Physics,
University of Yeditepe,
Turkey.
2Department
of Information Systems and Technologies,
University of Yeditepe,
Turkey
3Department
of Software Development,
University of Yeditepe,
Turkey.
4Laboratory
of Mathematics and their interactions,
University Center of Abdelhafid Boussouf,
Mila 43000,
Algeria.
E-mail:
berc890@gmail.com
ahacinliyan@yeditepe.edu.tr
engin.kandiran@yeditepe.edu.tr
cihan.keles@yeditepe.edu.tr
s.kaouache@centr-univ-mila.dz
medsalah3@yahoo.fr
n.hamri@centre-univ-mila.dz
Abstract:
In this article dynamical behavior of coupled Duffing oscillators is analyzed under a small modification. The oscillators have cubic damping instead of linear one. Although single duffing oscillator has complex dynamics, coupled duffing systems possess a much more complex structure. The dynamical behavior of the system is investigated both numerically and analytically. Numerical results indicate that the system has double scroll attractor with suitable parameter values. On the other hand, bifurcation diagrams illustrate rich behavior of the system, and it is seen that, system enters into chaos with different routes. Beside classical bifurcations, bubbling route to chaos is observed for suitable parameter settings. On the other hand, Multistability of the system is indicated with the coexisting attractors, such that under same parameter setting the system shows different periodic and chaotic attractors. Moreover, chaotic synchronization of coupled oscillators is illustrated in final section.
Paper's Title:
Three Inequalities Associated with Rado Inequality
Author(s):
Rin Miyao, Yusuke Nishizawa, Keigo Takamura
Faculty of Education,
Saitama University,
Shimo-okubo 255, Sakura-ku, Saitama-city, Saitama,
Japan.
E-mail: r.miyao.242@ms.saitama-u.ac.jp
Faculty of Education,
Saitama University,
Shimo-okubo 255, Sakura-ku, Saitama-city, Saitama,
Japan.
E-mail:
ynishizawa@mail.saitama-u.ac.jp
Faculty of Education,
Saitama University,
Shimo-okubo 255, Sakura-ku, Saitama-city, Saitama,
Japan.
E-mail: k.takamura.442@ms.saitama-u.ac.jp
Abstract:
In this short note we estimate three inequalities associated with Rado inequality and show the refinement and reverse of Arithmetic mean- Geometric mean inequality.
Paper's Title:
Reverse Hölder and Minkowski type integral inequalities for n functions
Author(s):
Panagiotis T. Krasopoulos and Lazhar Bougoffa
Department of Informatics, KEAO,
Electronic National Social Security Fund,
12 Patision St., 10677, Athens,
Greece.
E-mail: pan_kras@yahoo.gr
pankras@teemail.gr
Department of Mathematics,
Faculty of Science, Imam Mohammad Ibn Saud Islamic University,
P.O. Box 90950, Riyadh 11623,
Saudi Arabia.
E-mail: lbbougoffa@imamu.edu.sa
bougoffa@hotmail.com
Abstract:
We present and prove new reverse Hölder and Minkowski type integral inequalities for n functions. We compare our results with other known results from the relative literature in order to test their performance. In this respect, our theorems can be viewed as generalizations of some already known integral inequalities.
Paper's Title:
Boundness of the Power Exponential Function a2b +b2a
Author(s):
Yusuke Nishizawa, Yukuhito Yasuda
Faculty of Education, Saitama University,
Shimo-okubo 255, Sakura-ku, Saitama-city, Saitama,
Japan.
E-mail:
ynishizawa@mail.saitama-u.ac.jp
Faculty of Education, Saitama University,
Shimo-okubo 255, Sakura-ku, Saitama-city, Saitama,
Japan.
E-mail: y.yasuda.694@ms.saitama-u.ac.jp
Abstract:
In this paper, we consider the boundness of the power exponential function a2b +b2a for nonnegative real numbers a and b. The author proved that the function has the maximum value 1 for a + b = ½, but it is no known that the minimum value for a + b = ½. In this paper, we give the new proof of the function has the maximum value 1 and show that a2b +b2a > 0.989905 for a + b = ½.
Paper's Title:
On a Criteria for Strong Starlikeness
Author(s):
V. Ravichandran, M. Darus, and N. Seenivasagan
School Of Mathematical Sciences,
Universiti Sains Malaysia,
11800 Usm Penang, Malaysia
vravi@cs.usm.my
URL: http://cs.usm.my/~vravi
School of Mathematical Sciences, Faculty of Sciences and Technology,
Ukm, Bangi 43600, Malaysia
maslina@pkrisc.cc.ukm.my
Sindhi College, 123, P. H. Road, Numbal,
Chennai 600 077 India
vasagan2000@yahoo.co.in
Abstract:
In this paper, we are concerned with finding sufficient condition for certain normalized analytic function f(z) defined on the open unit disk in the complex plane to be strongly starlike of order
α. Also we have obtained similar results for certain functions defined by Ruscheweyh derivatives and Sălăgean derivatives. Further extension of these results are given for certain p-valent analytic functions defined through a linear operator.
Paper's Title:
q-Norms are Really Norms
Author(s):
H. Belbachir, M. Mirzavaziri and M. S. Moslehian
USTHB, Faculté de Mathématiques,
B.P. 32, El Alia, 16111,
Bab Ezzouar, Alger,
Algérie.
hbelbachir@usthb.dz
Department of Mathematics,
Ferdowsi University, P. O. Box 1159,
Mashhad 91775, Iran.
mirzavaziri@math.um.ac.ir
URL: http://www.mirzavaziri.com
Department of Mathematics,
Ferdowsi University,
P. O. Box 1159,
Mashhad 91775, Iran.
moslehian@ferdowsi.um.ac.ir
URL: http://www.um.ac.ir/~moslehian/
Abstract:
Replacing the triangle inequality, in the definition of a
norm, by 
, we introduce the notion of a q-norm. We establish that
every q-norm is a norm in the usual sense, and that the converse is true as
well.
Paper's Title:
A Dynamic Contact Problem for an Electro Viscoelastic Body
Author(s):
Denche M. and Ait Kaki L.
Laboratoire Equations Differentielles,
Departement de Mathematiques,
Universite Constantine 1,
Algeria.
Ecole Normale Superieure,
Departement des Sciences Exactes et Informatique,
Plateau Mansourah, Constantine.
Algeria.
E-mail:
m.denche@umc.edu.dz
leilaitkaki@yahoo.fr
Abstract:
We consider a dynamic problem which describes a contact between a piezoelectric body and a conductive foundation. The frictionless contact is modelled with the normal compliance, the electric conditions are supposed almost perfect. We prove the existence of a unique weak solution for almost perfect electric contact.
Paper's Title:
A Unifying View of Some Banach Algebras
Author(s):
R. Kantrowitz
Mathematics & Statistics Department,
Hamilton College,
198 College Hill Road,
Clinton, NY 13323, USA.
E-mail: rkantrow@hamilton.edu
Abstract:
The purpose of this article is to shed light on a unifying framework for some normed algebras and, in particular, for some Banach algebras. The focus is on linear operators T between normed algebras X and Y and specified subalgebras A of Y. When the action of T on products in X satisfies a certain operative equation, the subspace T-1(A) is stable under the multiplication of X and is readily equipped with a family of canonical submultiplicative norms. It turns out that many familiar and important spaces are encompassed under this versatile perspective, and we offer a sampling of several such. In this sense, the article presents an alternative lens through which to view a host of normed algebras. Moreover, recognition that a normed linear space conforms to this general structure provides another avenue to confirming that it is at once stable under multiplication and also outfitted with an abundance of equivalent submultiplicative norms.
Paper's Title:
On Sufficient Conditions for Strong Starlikeness
Author(s):
V. Ravichandran, M. H. Khan, M. Darus, And
K. G. Subramanian School of Mathematical Sciences, Universiti Sains Malaysia,
11800 Usm Penang, Malaysia
vravi@cs.usm.my
Url: http://cs.usm.my/~vravi/index.html
Department of Mathematics, Islamiah College, Vaniambadi 635 751, India
khanhussaff@yahoo.co.in
School of Mathematical Sciences, Faculty of Science and Technology, UKM, Bangi
43600,
Malaysia
maslina@pkrisc.cc.ukm.my
Url:
http://www.webspawner.com/users/maslinadarus
Department of Mathematics, Madras Christian College, Tambaram, Chennai 600 059,
India
kgsmani@vsnl.net
Abstract:
In the present investigation, we obtain some sufficient
conditions for a normalized analytic function f(z) defined on the unit disk to
satisfy the condition
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:
A New Step Size Rule in Noor's Method for Solving General Variational Inequalities
Author(s):
Abdellah Bnouhachem
School of Management Science and Engineering, Nanjing University,
Nanjing, 210093
P.R. China.
babedallah@yahoo.com
Abstract:
In this paper, we propose a new step size rule in Noor's method
for solving general
variational inequalities. Under suitable conditions, we prove that the
new method is globally convergent. Preliminary numerical
experiments are included to illustrate the advantage and
efficiency of the proposed method.
Paper's Title:
On Pseudo Almost
Periodic Solutions to Some Neutral Functional-Differential
Equations
Author(s):
Toka Diagana and Eduardo Hernández
Department of Mathematics, Howard University
2441 6th Street NW,
Washington DC 20059,
USA.
tdiagana@howard.edu
Departamento de Matemática, I.C.M.C. Universidade de São Paulo,
Caixa Postal
668, 13560-970, São Carlos SP,
Brazil.
lalohm@icmc.sc.usp.br
Abstract:
This paper discusses the existence and uniqueness of pseudo almost periodic solutions to a class of partial neutral functional-differential equations. Under some suitable assumptions, existence and uniqueness results are obtained. An example is given to illustrate abstract results.
Paper's Title:
A Nonlinear Proximal Alternating Directions Method for Structured Variational Inequalities
Author(s):
M. Li
Department of Management Science and Engineering, School of Economics and Management
Southeast University, Nanjing, 210096,
China.
liminnju@yahoo.com
Abstract:
In this paper, we present a nonlinear proximal alternating directions method (NPADM) for solving a class of structured variational inequalities (SVI). By choosing suitable Bregman functions, we generalize the proximal alternating directions method proposed by He, et al.. The convergence of the method is proved under quite mild assumptions and flexible parameter conditions.
Paper's Title:
Some Inequalities for a Certain Class of Multivalent Functions
Using Multiplier Transformation
Author(s):
K. Suchithra, B. Adolf Stephen, A. Gangadharan and S. Sivasubramanian
Department Of Applied Mathematics
Sri Venkateswara College Of Engineering
Sriperumbudur, Chennai - 602105,
India.
suchithravenkat@yahoo.co.in
Department Of Mathematics,
Madras Christian College
Chennai - 600059,
India.
adolfmcc2003@yahoo.co.in
Department Of Applied Mathematics
Sri Venkateswara College Of Engineering
Sriperumbudur, Chennai - 602105,
India.
ganga@svce.ac.in
Department Of Mathematics,
Easwari Engineering College
Ramapuram, Chennai - 600089,
India.
ganga@svce.ac.in
Abstract:
The object of the present paper is to derive several inequalities
associated with differential subordinations between analytic functions
and a linear operator defined for a certain family of p-valent
functions, which is introduced here by means of a family of extended
multiplier transformations. Some special cases and consequences of
the main results are also considered.
Paper's Title:
Some Generalized Difference Sequence Spaces Defined by Orlicz Functions
Author(s):
Ramzi S. N. Alsaedi and Ahmad H. A. Bataineh
Department of Mathematics, King Abdul Aziz University,
Jeddah P.O.Box 80203,
Saudia Arabia
ramzialsaedi@yahoo.co.uk
Department of Mathematics, Al al-Bayt University,
Mafraq 25113,
Jordan
ahabf2003@yahoo.ca
Abstract:
In this paper, we define the sequence spaces: [V,M,p,u,Δ ],[V,M,p,u,Δ]0 and
[V,M,p,u,Δ]∞, where for any sequence x=(xn),
the difference sequence Δx is given by Δx=(Δxn)
= (xn-xn-1) . We also study some properties and theorems of
these spaces. These are generalizations of those defined and studied by
Savas and Savas and some others before.
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,
Department of Technical Cybernetics,
Dipartimento di Ingegneria dell'Informazione e Matematica Applicata,
Via Ponte don Melillo, 84084 Fisciano (SA),
Italy
manzo@diima.unisa.it
Dnipropetrovsk Technical University,
Acad. Lazarjan
STR., 2,
49010 Dnipropetrovsk,
Ukraine
i.nechay@i.ua
Abstract:
In this paper, we study vector optimization problems in partially ordered Banach spaces. We suppose that the objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. We derive sufficient conditions for existence of efficient solutions of the above problems and discuss the role of topological properties of the objective space. We discuss the scalarization of vector optimization problems when the objective functions are vector-valued mappings with a weakened property of lower semicontinuity. We also prove the existence of the so-called generalized efficient solutions via the scalarization process. All principal notions and assertions are illustrated by numerous examples.
Paper's Title:
On Eigenvalues and Boundary Curvature of the C*-algebra Numerical Rang
Author(s):
M. T. Heydari
Department of Mathematics,
College of Sciences,
Yasouj University,
Yasouj, 75914-74831,
Iran.
E-mail: heydari@yu.ac.ir
Abstract:
Let A be a C*-algebra with unit 1 and a∈A be a nilpotent. By Donoghue's Theorem, all corner points of its numerical range V(a) belong to the spectrum σ(a). It is therefore natural to expect that, more generally, the distance from a point p on the boundary ∂ V(a) of V(a) to σ(a) should be in some sense bounded by the radius of curvature of ∂ V(a) at p.
Paper's Title:
Strong Convergence Theorem for a Common Fixed Point of an
Infinite Family of J-nonexpansive Maps with Applications
Author(s):
Charlse Ejike Chidume, Otubo Emmanuel Ezzaka and Chinedu Godwin Ezea
African University of Science and
Technology,
Abuja,
Nigeria.
E-mail:
cchidume@aust.edu.ng
Ebonyi State University,
Abakaliki,
Nigeria.
E-mail: mrzzaka@yahoo.com
Nnamdi Azikiwe University,
Awka,
Nigeria.
E-mail: chinedu.ezea@gmail.com
Abstract:
Let E be a uniformly convex and uniformly smooth real Banach space with dual space E*. Let {Ti}∞i=1 be a family of J-nonexpansive maps, where, for each i,~Ti maps E to 2E*. A new class of maps, J-nonexpansive maps from E to E*, an analogue of nonexpansive self maps of E, is introduced. Assuming that the set of common J-fixed points of {Ti}∞i=1 is nonempty, an iterative scheme is constructed and proved to converge strongly to a point x* in ∩∞n=1FJTi. This result is then applied, in the case that E is a real Hilbert space to obtain a strong convergence theorem for approximation of a common fixed point for an infinite family of nonexpansive maps, assuming existences. The theorem obtained is compared with some important results in the literature. Finally, the technique of proof is also of independent interest.
Paper's Title:
Iterative Approximation of Zeros of Accretive Type Maps, with Applications
Author(s):
Charles Ejike Chidume, Chinedu Godwin Ezea, and Emmanuel Ezzaka Otubo
African University of Science and
Technology, Abuja,
Nigeria.
E-mail: cchidume@aust.edu.ng
E-mail: chinedu.ezea@gmail.com
E-mail: mrzzaka@yahoo.com
Department of Mathematics,
Nnamdi Azikiwe University,
Awka,
Nigeria
E-mail: chinedu.ezea@gmail.com
Ebonyi State University,
Abakaliki,
Nigeria
E-mail: mrzzaka@yahoo.com
Abstract:
Let E be a reflexive real Banach space with uniformly Gâteaux differentiable norm. Let J:E→ E* be the normalized duality map on E and let A:E*→ E be a map such that AJ is an accretive and uniformly continuous map. Suppose that (AJ)-1(0) in nonempty. Then, an iterative sequence is constructed and proved to converge strongly to some u* in (AJ)-1(0). Application of our theorem in the case that E is a real Hilbert space yields a sequence which converges strongly to a zero of A. Finally, non-trivial examples of maps A for which AJ is accretive are presented..
Paper's Title:
Introducing the Dorfmanian: A Powerful Tool for the Calculus Of Variations
Author(s):
Olivier de La Grandville
Department of Management Science and Engineering,
Stanford University,
475 Via Ortega, Stanford, CA 94305,
U. S. A.
E-mail: odelagrandville@gmail.com
Abstract:
We show how a modified Hamiltonian proposed by Robert Dorfman [1] to give intuitive sense
to the Pontryagin maximum principle can be extended to easily obtain all
high-order equations of the calculus of variations. This new concept is
particularly efficient to determine the differential equations leading to
the extremals of functionals defined by n-uple integrals, while a
traditional approach would require -- in some cases repeatedly -- an
extension of Green's theorem to n-space.
Our paper is dedicated to the memory of Robert Dorfman (1916 - 2002).
Paper's Title:
Higher Order Accurate Compact Schemes for Time Dependent Linear and Nonlinear Convection-Diffusion Equations
Author(s):
S. Thomas, Gopika P.B. and S. K. Nadupuri
Department of Mathematics
National Institute of Technology Calicut
Kerala
673601
India.
E-mail:
sobinputhiyaveettil@gmail.com
pbgopika@gmail.com nsk@nitc.ac.in
Abstract:
The primary objective of this work is to study higher order compact finite difference schemes for finding the numerical solution of convection-diffusion equations which are widely used in engineering applications. The first part of this work is concerned with a higher order exponential scheme for solving unsteady one dimensional linear convection-diffusion equation. The scheme is set up with a fourth order compact exponential discretization for space and cubic $C^1$-spline collocation method for time. The scheme achieves fourth order accuracy in both temporal and spatial variables and is proved to be unconditionally stable. The second part explores the utility of a sixth order compact finite difference scheme in space and Huta's improved sixth order Runge-Kutta scheme in time combined to find the numerical solution of one dimensional nonlinear convection-diffusion equations. Numerical experiments are carried out with Burgers' equation to demonstrate the accuracy of the new scheme which is sixth order in both space and time. Also a sixth order in space predictor-corrector method is proposed. A comparative study is performed of the proposed schemes with existing predictor-corrector method. The investigation of computational order of convergence is presented.
Paper's Title:
Notes on Sakaguchi Functions
Author(s):
Shigeyoshi Owa, Tadayuki Sekine and Rikuo Yamakawa
Department of Mathematics, Kinki University,
Higashi-Osaka, Osaka 577-8502,
Japan.
owa@math.kindai.ac.jp
Office of Mathematics, College of Pharmacy, Nihon University,
7-1 Narashinodai, Funabashi-city,
Chiba, 274-8555, Japan.
tsekine@pha.nihon-u.ac.jp
Department of Mathematics, Shibaura Institute of Technology,
Minuma, Saitama-city,
Saitama 337-8570, Japan.
yamakawa@sic.shibaura-it.ac.jp
Abstract:
By using the definition for certain
univalent functions f(z) in the open unit disk U given by K. Sakaguchi
[2], two classes S(α) and T(α) of analytic functions in U
are introduced. The object of the present paper is to discuss some properties of
functions f(z) belonging to the classes S(α) and T(α).
Paper's Title:
Existence of solutions for Neutral Stochastic Functional Differential Systems with Infinite Delay in Abstract Space
Author(s):
P. Balasubramaniam, A. V. A. Kumar and S. K. Ntouyas
Department of Mathematics, Gandhigram Rural Institute,
Deemed University, Gandhigram - 624 302,
Tamil Nadu, India.
pbalgri@rediffmail.com
Department of Mathematics, Gandhigram Rural Institute,
Deemed University, Gandhigram - 624 302,
Tamil Nadu, India.
nnddww@tom.com
Department of Mathematics, University of Ioannina,
451 10 Ioannina,
Greece.
sntouyas@cc.uoi.gr
URL: http://www.math.uoi.gr/~sntouyas
Abstract:
In this paper we prove existence results for semilinear stochastic neutral functional differential systems with unbounded delay in abstract space. Our theory makes use of analytic semigroups and fractional power of closed operators and Sadovskii fixed point theorem.
Paper's Title:
Local and Global Existence and Uniqueness Results for Second and Higher Order Impulsive Functional Differential Equations with Infinite Delay
Author(s):
Johnny Henderson and Abdelghani Ouahab
Department of Mathematics, Baylor University,
Waco, Texas 76798-7328
USA.
Johnny_Henderson@baylor.edu
Laboratoire de Mathématiques, Université de Sidi Bel Abbés
BP 89, 22000 Sidi Bel Abbées,
Algérie.
ouahab@univ-sba.dz
Abstract:
In this paper, we discuss the local and global existence and
uniqueness results for second and higher order impulsive functional
differential equations with infinite delay. We shall rely on a
nonlinear alternative of Leray-Schauder. For the global existence
and uniqueness we apply a recent Frigon and Granas nonlinear
alternative of Leray-Schauder type in Fréchet spaces.
Paper's Title:
Equilibria and Periodic Solutions of Projected Dynamical Systems on Sets with Corners
Author(s):
Matthew D. Johnston and Monica-Gabriela Cojocaru
Department of Applied Mathematics, University of Waterloo,
Ontario, Canada
mdjohnst@math.uwaterloo.ca
Department of Mathematics & Statistics, University of
Guelph,
Ontario, Canada
mcojocar@uoguelph.ca
Abstract:
Projected dynamical systems theory represents a bridge between the
static worlds of variational inequalities and equilibrium
problems, and the dynamic world of ordinary differential
equations. A projected dynamical system (PDS) is given by the flow
of a projected differential equation, an ordinary differential
equation whose trajectories are restricted to a constraint set
K. Projected differential equations are defined by discontinuous
vector fields and so standard differential equations theory cannot
apply. The formal study of PDS began in the 90's, although some
results existed in the literature since the 70's. In this paper we
present a novel result regarding existence of equilibria and
periodic cycles of a finite dimensional PDS on constraint sets
K, whose points satisfy a corner condition. The novelty is due
to proving existence of boundary equilibria without using a
variational inequality approach or monotonicity type conditions.
Paper's Title:
Applications of Relations and Relators in the
Extensions of Stability Theorems for Homogeneous and Additive Functions
Author(s):
Árpád Száz
Institute of Mathematics, University of Debrecen,
H-4010 Debrecen,
Pf. 12,
Hungary
szaz@math.klte.hu
Abstract:
By working out an appropriate technique of relations and relators and extending the ideas of the direct methods of Z. Gajda and R. Ger, we prove some generalizations of the stability theorems of D. H. Hyers, T. Aoki, Th. M. Rassias and P. Găvruţă in terms of the existence and unicity of 2-homogeneous and additive approximate selections of generalized subadditive relations of semigroups to vector relator spaces. Thus, we obtain generalizations not only of the selection theorems of Z. Gajda and R. Ger, but also those of the present author.
Paper's Title:
Hyers-Ulam-Rassias Stability
of a Generalized Jensen Functional Equation
Author(s):
A. Charifi, B. Bouikhalene, E. Elqorachi and A. Redouani
Department of
Mathematics, Faculty of Sciences,
Ibn Tofail University,
Kenitra, Morocco
charifi2000@yahoo.fr
bbouikhalene@yahoo.fr
Department of
Mathematics, Faculty of Sciences,
Ibn Zohr University,
Agadir, Morocco
elqorachi@hotmail.com
Redouani-ahmed@yahoo.fr
Abstract:
In this paper we obtain the Hyers-Ulam-Rassias stability for the generalized Jensen's functional equation in abelian group (G,+). Furthermore we discuss the case where G is amenable and we give a note on the Hyers-Ulam-stability of the K-spherical (n × n)-matrix functional equation.
Paper's Title:
Generalized Efficient Solutions to One Class of Vector Optimization Problems in Banach Space
Author(s):
Peter I. Kogut, Rosanna Manzo, and Igor V. Nechay
Department of Differential Equations,
Dnipropetrovsk National University,
Naukova str., 13,
49050 Dnipropetrovsk,
Ukraine
p.kogut@i.ua
Dipartimento di Ingegneria
Dell’informazione e Matematica Applicata,
Università di Salerno,
Via
Ponte
Don Melillo,
84084 Fisciano
(Sa),
Italy
manzo@diima.unisa.it
Department of Technical Cybernetics,
Dnipropetrovsk Technical University,
Acad. Lazarjan str., 2,
49010
Dnipropetrovsk,
Ukraine
i.nechay@i.ua
Abstract:
In this paper, we study vector optimization problems in Banach spaces for essentially nonlinear operator equations with additional control and state constraints. We assume that an objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. Using the penalization approach we derive both sufficient and necessary conditions for the existence of efficient solutions of the above problems. We also prove the existence of the so-called generalized efficient solutions via the scalarization of some penalized vector optimization problem.
Paper's Title:
Real Interpolation Methods and Quasilogarithmic Operators
Author(s):
Ming Fan
School of Industrial Technology and Management,
Dalarna University, 781 88 Borlänge, Sweden
fmi@du.se
URL: http://users.du.se/~fmi
Abstract:
The purpose of this paper is to deal with nonlinear quasilogarithmic operators, which possesses the uniformly bounded commutator property on various interpolation spaces in the sense of Brudnyi-Krugljak associated with the quasi-power parameter spaces. The duality, and the domain and range spaces of these operators are under consideration. Some known inequalities for the Lebesgue integration spaces and the trace classes are carried over to the non-commutative symmetric spaces of measurable operators affiliated with a semi-finite von Neumann algebra.
Paper's Title:
Existence Results for Second Order Impulsive Functional Differential Equations with Infinite Delay
Author(s):
M. Lakrib, A. Oumansour and K. Yadi
Laboratoire de Mathématiques, Université Djillali
Liabées, B.P. 89 Sidi Bel Abbès 22000, Algérie
mlakrib@univ-sba.dz
oumansour@univ-sba.dz
Laboratoire de Mathématiques, Université Abou Bekr
Belkaid, B.P. 119 Tlemcen 13000, Algérie
k_yadi@mail.univ-tlemcen.dz
Abstract:
In this paper we study the existence of solutions for second order impulsive functional differential equations with infinite delay. To obtain our results, we apply fixed point methods.
Paper's Title:
On Generalized Triangle Inequality in p-Freéchet Spaces, 0<p<1
Author(s):
M. A. Latif
Department of Mathematics,
University of Hail, Hail,
Saudi Arabia
m_amer_latif@hotmail.com
Abstract:
In this paper generalized triangle inequality and its reverse in a p-Fréchet space where, 0<p<1 are obtained.
Paper's Title:
To a Banach *-algebra in a Semipartial Dynamical System
Author(s):
Bahman Tabatabaie Shourijeh and Seyed Mostafa Zebarjad
Department of Mathematics,
College of Sciences,
Shiraz University, Shiraz 71454,
Iran.
E-mail:
tabataba@math.susc.ac.ir
zebarjad@mail.yu.ac.ir
URL:
http://research.shirazu.ac.ir/faculty/More.asp?ID=207
Abstract:
By a partial dynamical system, we mean a triple containing a C*-algebra A, a discrete group G and a partial action of G on A. There are two C*--algebras associated to a given partial dynamical system. These are nothing but the certain C*-completions of a Banach *-algebra. In constructing such a Banach *-algebra, usually, a tedious limit process is used to apply. In this paper, we prove some theorems in this context without any limit process.
Paper's Title:
Application of Equivalence Method to Classify Monge-Ampère Equations of Elliptic Type
Author(s):
Moheddine Imsatfia
E-mail: imsatfia@math.jussieu.fr
Abstract:
In this paper, we apply Cartan's equivalence method to give a local classification of Monge-Ampère equations of elliptic type. Then we find a necessary and sufficient conditions such that a Monge-Ampère equation is either contactomorphic to the Laplace equation or to an Euler-Lagrange equation.
Paper's Title:
Asymptotic Analysis of Positive Decreasing Solutions of a Class of Systems of Second Order Nonlinear Differential Equations in the Framework of Regular Variation
Author(s):
Jaroslav Jaroš, Kusano Takaŝi, Tomoyuki Tanigawa
Department of Mathematical Analysis and
Numerical Mathematics,
Faculty of Mathematics, Physics and Informatics,
Comenius Universiy, 842 48 Bratislava,
Slovakia.
E-mail: ksntksjm4@gmail.com
Professor Emeritus at: Hiroshima
University,
Department of Mathematics, Faculty of Science,
Higashi-Hiroshima 739-8526,
Japan.
E-mail: jaros@fmph.uniba.sk
Department of Mathematics, Faculty of
Education,
Kumamoto University, Kumamoto 860-8555,
Japan.
E-mail:
tanigawa@educ.kumamoto-u.ac.jp
Abstract:
The system of nonlinear differential equations
is under consideration, where αi
and βi are positive constants and
pi(t) and qi(t) are continuous regularly varying functions
on [a,∞). Two kinds of criteria are established for
the existence of strongly decreasing regularly varying solutions with negative
indices of (A) with precise asymptotic behavior at infinity. Fixed point
techniques and basic theory of regular variation are utilized for this purpose.
Paper's Title:
Credibility Based Fuzzy Entropy Measure
Author(s):
G. Yari, M. Rahimi, B. Moomivand and P. Kumar
Department of Mathematics,
Iran University
of Science and Technology,
Tehran,
Iran.
E-mail:
Yari@iust.ac.ir
E-mail:
Mt_Rahimi@iust.ac.ir
URL:
http://www.iust.ac.ir/find.php?item=30.11101.20484.en
URL:
http://webpages.iust.ac.ir/mt_rahimi/en.html
Qarzol-hasaneh
Mehr Iran Bank, Tehran,
Iran.
E-mail:
B.moomivand@qmb.ir
Department of Mathematics and Statistics,
University of Northern British Columbia,
Prince George, BC,
Canada.
E-mail:
Pranesh.Kumar@unbc.ca
Abstract:
Fuzzy entropy is the entropy of a fuzzy variable, loosely representing the information of uncertainty. This paper, first examines both previous membership and credibility based entropy measures in fuzzy environment, and then suggests an extended credibility based measure which satisfies mostly in Du Luca and Termini axioms. Furthermore, using credibility and the proposed measure, the relative entropy is defined to measure uncertainty between fuzzy numbers. Finally we provide some properties of this Credibility based fuzzy entropy measure and to clarify, give some examples.
Paper's Title:
Coefficient Estimates for Certain Subclasses of Bi-univalent Sakaguchi
Type Functions by using Faber Polynomial
Author(s):
P. Murugabharathi, B. Srutha Keerthi
Mathematics Division,
School of Advanced Sciences,
VIT Chennai, Vandaloor, Kelambakkam Road,
Chennai - 600 127, India.
E-mail: bharathi.muhi@gmail.com
E-mail: sruthilaya06@yahoo.co.in
Abstract:
In this work, considering a general subclass of bi-univalent Sakaguchi type functions, we determine estimates for the general Taylor-Maclaurin coefficients of the functions in these classes. For this purpose, we use the Faber polynomial expansions. In certain cases, our estimates improve some of those existing coefficient bounds.
Paper's Title:
Inequalities for Discrete F-Divergence Measures: A Survey of Recent Results
Author(s):
Sever S. Dragomir1,2
1Mathematics, School of Engineering
& Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au
2DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL:
http://rgmia.org/dragomir
Abstract:
In this paper we survey some recent results obtained by the author in providing various bounds for the celebrated f-divergence measure for various classes of functions f. Several techniques including inequalities of Jensen and Slater types for convex functions are employed. Bounds in terms of Kullback-Leibler Distance, Hellinger Discrimination and Varation distance are provided. Approximations of the f-divergence measure by the use of the celebrated Ostrowski and Trapezoid inequalities are obtained. More accurate approximation formulae that make use of Taylor's expansion with integral remainder are also surveyed. A comprehensive list of recent papers by several authors related this important concept in information theory is also included as an appendix to the main text.
Paper's Title:
Countable Ordinal Spaces and Compact Countable Subsets of a Metric Space
Author(s):
B. Alvarez-Samaniego, A. Merino
Nucleo de Investigadores Cientificos
Facultad de Ciencias,
Universidad Central del Ecuador (UCE)
Quito,
Ecuador.
E-mail: borys_yamil@yahoo.com,
balvarez@uce.edu.ec
Escuela de Ciencias Fisicas y Matematica
Facultad de Ciencias Exactas y Naturales
Pontificia Universidad Catolica del Ecuador
Apartado: 17-01-2184, Quito,
Ecuador.
E-mail: aemerinot@puce.edu.ec
Abstract:
We show in detail that every compact countable subset of a metric space is homeomorphic to a countable ordinal number, which extends a result given by Mazurkiewicz and Sierpinski for finite-dimensional Euclidean spaces. In order to achieve this goal, we use Transfinite Induction to construct a specific homeomorphism. In addition, we prove that for all metric space, the cardinality of the set of all the equivalence classes, up to homeomorphisms, of compact countable subsets of this metric space is less than or equal to aleph-one. We also show that for all cardinal number smaller than or equal to aleph-one, there exists a metric space with cardinality equals the aforementioned cardinal number.
Paper's Title:
A new approach to the study of fixed point for simulation functions with application in G-metric spaces
Author(s):
Komi Afassinou and Ojen Kumar Narain
Department of Mathematical Sciences,
University of Zululand,
KwaDlangezwa,
South Africa.
E-mail: komia@aims.ac.za
School of Mathematics, Statistics and
Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: naraino@ukzn.ac.za
Abstract:
The purpose of this work is to generalize the fixed point results of Kumar et al. [11] by introducing the concept of (α,β)-Z-contraction mapping, Suzuki generalized (α,β)-Z-contraction mapping, (α,β)-admissible mapping and triangular (α,β)-admissible mapping in the frame work of G-metric spaces. Fixed point theorems for these class of mappings are established in the frame work of a complete G-metric spaces and we establish a generalization of the fixed point result of Kumar et al. [11] and a host of others in the literature. Finally, we apply our fixed point result to solve an integral equation.
Paper's Title:
Attempts to Define a Baum--Connes Map Via Localization of Categories for Inverse Semigroups
Author(s):
Bernhard Burgstaller
Departamento de Matematica,
Universidade Federal de Santa Catarina,
CEP 88.040-900 Florianopolis-SC,
Brasil.
E-mail:
bernhardburgstaller@yahoo.de
URL:
http://mathematik.work/bernhardburgstaller/index.html
Abstract:
An induction functor in inverse semigroup equivariant KK-theory is considered, and together with %a restriction functors certain results similar to those known from the Mackey machinery are shown. It is also verified that for any so-called E-continuous inverse semigroup its equivariant KK-theory satisfies the universal property and is a triangulated category.
Paper's Title:
The Effect of Harvesting Activities on Prey-Predator Fishery Model with Holling type II in Toxicant Aquatic Ecosystem
Author(s):
Moh Nurul Huda, Fidia Deny Tisna Amijaya, Ika Purnamasari
Department of Mathematics, Faculty of
Mathematics and Natural Science,
Mulawarman University,
Samarinda, East Kalimantan,75123
Indonesia.
E-mail: muh.nurulhuda@fmipa.unmul.ac.id
fidiadta@fmipa.unmul.ac.id
ika.purnamasari@fmipa.unmul.ac.id
Abstract:
This paper discussed prey-predator fishery models, in particular by analysing the effects of toxic substances on aquatic ecosystems. It is assumed in this model, that the prey population is plankton and the predator population is fish.\ Interaction between the two populations uses the Holling type II function. The existence of local and global critical points of the system are shown and their stability properties are analysed. Furthermore, Bionomic equilibrium and optimal control of harvesting are discussed. Finally, numerical simulations have been carried out to show in the interpretation of results.
Paper's Title:
A Self-adaptive Subgradient Extragradient Algorithm for Variational Inequality Problems and Fixed Point Problems in Banach Spaces
Author(s):
F. U. Ogbuisi
School of Mathematics, Statistics and
Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
Department of Mathematics,
University of Nigeria, Nsukka,
Nigeria.
E-mail: ferdinard.ogbuisi@unn.edu.ng
fudochukwu@yahoo.com
Abstract:
In this paper, we propose and analyze a type of subgradient extragradient algorithm for the approximation of a solution of variational inequality problem which is also a common fixed point of an infinite family of relatively nonexpansive mappings in 2-uniformly convex Banach spaces which are uniformly smooth. By using the generalized projection operator, we prove a strong convergence theorem which does not require the prior knowledge of the Lipschitz constant of cost operator. We further applied our result to constrained convex minimization problem, convex feasibility problem and infinite family of equilibrium problems. Our results improve and complement related results in 2-uniformly convex and uniformly smooth Banach spaces and Hilbert spaces.
Paper's Title:
Sweeping Surfaces with Darboux Frame in Euclidean 3-space E3
Author(s):
F. Mofarreh, R. Abdel-Baky and N. Alluhaibi
Mathematical Science Department, Faculty
of Science,
Princess Nourah bint Abdulrahman University
Riyadh 11546,
Saudi Arabia.
E-mail: fyalmofarrah@pnu.edu.sa
Department of Mathematics, Faculty of Science,
University of Assiut,
Assiut 71516,
Egypt.
E-mail: rbaky@live.com
Department of Mathematics Science and
Arts, College Rabigh Campus,
King Abdulaziz University
Jeddah,
Saudi Arabia.
E-mail: nallehaibi@kau.edu.sa
Abstract:
The curve on a regular surface has a moving frame and it is called Darboux frame. We introduce sweeping surfaces along the curve relating to the this frame and investigate their geometrical properties. Moreover, we obtain the necessary and sufficient conditions for these surfaces to be developable ruled surfaces. Finally, an example to illustrate the application of the results is introduced.
Paper's Title:
On Admissible Mapping via Simulation Function
Author(s):
Anantachai Padcharoen and Pakeeta Sukprasert
Department of Mathematics,
Faculty of Science and Technology,
Rambhai Barni Rajabhat University,
Chanthaburi 22000,
Thailand.
E-mail: anantachai.p@rbru.ac.th
Department of Mathematics and Computer Science
Faculty of Science and Technology
Rajamangala University of Technology Thanyaburi (RMUTT),
Thanyaburi, Pathumthani 12110,
Thailand.
E-mail: pakeeta_s@rmutt.ac.th
Abstract:
In this paper, we present some fixed point results in complete metric spaces by using generalized admissible mapping embedded in the simulation function. Its applications, Our results used to study the existence problem of nonlinear Hammerstein integral equations.
Paper's Title:
Pointwise Convergence of Fourier-type Series with Exponential Weights
Author(s):
Hee Sun Jung and Ryozi Sakai
Department of Mathematics Education,
Sungkyunkwan University,
Seoul 110-745,
Republic of Korea.
E-mail: hsun90@skku.edu
Department of Mathematics,
Meijo University, Nagoya 468-8502,
Japan.
E-mail: ryozi@hm.aitai.ne.jp
Abstract:
Let R = ( - ∞,∞), and let Q∈C1(R):R→[0,∞) be an even function. We consider the exponential weights w(x)=e-Q(x), x∈R. In this paper we obtain a pointwise convergence theorem for the Fourier-type series with respect to the orthonormal polynomials {pn(w2;x)}.
Paper's Title:
Existence of Solution of Differential and Riemann-Liouville Equation Via Fixed Point Approach in Complex Valued b-Metric Spaces
Author(s):
K. Afassinou, A. A. Mebawondu, H. A. Abass and O. K. Narain
Department of Science Access,
University of Zululand, KwaDlangezwa,
South Africa.
E-mail: komia@aims.ac.za
DST-NRF Centre of Excellence in
Mathematical and Statistical Sciences (CoE-MaSS),
Johannesburg,
South Africa.
E-mail: dele@aims.ac.za
DST-NRF Centre of Excellence in
Mathematical and Statistical Sciences (CoE-MaSS),
Johannesburg,
South Africa.
E-mail: hammedabass548@gmail.com
School of Mathematics, Statistics and
Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: naraino@ukzn.ac.za
Abstract:
In this paper, we establish some fixed point and common fixed point results for a new type of generalized contractive mapping using the notion of C-class function in the framework of complex valued b-metric spaces. As an application, we establish the existence and uniqueness of a solution for Riemann-Liouville integral and ordinary differential equation in the framework of a complete complex valued b-metric spaces. The obtained results generalize and improve some fixed point results in the literature.
Paper's Title:
On General Class of Nonlinear Contractive Maps and their Performance Estimates
Author(s):
Olalekan Taofeek Wahab and Salaudeen Alaro Musa
Department of Mathematics and
Statistics
Kwara State University, Malete
P. M. B. 1530 Ilorin,
Nigeria.
E-mail: taofeek.wahab@kwasu.edu.ng
Abstract:
This paper considers two independent general class of nonlinear contractive maps to study the existence properties of nonlinear operators with prior degenerate. The existence properties are proved in the framework of approximate fixed points with the imposition of the general class of contractive conditions in metrical convex spaces without emphasis on completeness or compactness. For computational purposes, the performance estimates and the sensitivity dependence of these conditions are obtained for the Picard operator. Practical examples are also considered to justify the validity of the conditions. The results ensure no term is lost in the operators with prior degenerate and the conditions are strictly larger class when compare with others in the literature.
Paper's Title:
Some Moduli and Inequalities Related to Birkhoff Orthogonality in Banach Spaces
Author(s):
Dandan Du and Yongjin Li
Department of Mathematics,
Sun Yat-sen University,
Guangzhou, 510275,
P.R. China.
E-mail: dudd5@mail2.sysu.edu.cn
Department of Mathematics,
Sun Yat-sen University,
Guangzhou, 510275,
P.R. China.
E-mail: stslyj@mail.sysu.edu.cn
Abstract:
In this paper, we shall consider two new constants δB(X) and ρB(X), which are the modulus of convexity and the modulus of smoothness related to Birkhoff orthogonality, respectively. The connections between these two constants and other well-known constants are established by some equalities and inequalities. Meanwhile, we obtain two characterizations of Hilbert spaces in terms of these two constants, study the relationships between the constants δB(X), ρB(X) and the fixed point property for nonexpansive mappings. Furthermore, we also give a characterization of the Radon plane with affine regular hexagonal unit sphere.
Paper's Title:
Optimal Conditions using Multi-valued G-Presic type Mapping
Author(s):
Deb Sarkar, Ramakant Bhardwaj, Vandana Rathore, and Pulak Konar
Department of Mathematics, Amity
University, Kadampukur, 24PGS(N), Kolkata, West Bengal, 700135,
India.
E-mail: debsarkar1996@gmail.com
Department of Mathematics, Amity
University, Kadampukur, 24PGS(N), Kolkata, West Bengal, 700135,
India.
E-mail: drrkbhardwaj100@gmail.com
School of Engineering and Technology,
Jagran Lakecity University, Bhopal, MP-462044,
India.
E-mail: drvandana@jlu.edu.in
Department of Mathematics,
VIT University, Chennai, Tamil Nadu-600127,
India.
E-mail: pulakkonar@gmail.com
Abstract:
In the present paper, some best proximity results have been presented using the concept of G-Presic type multi-valued mapping. These results are the extensions of Presic's theorem in the non-self mapping. A suitable example has also been given. Here, some applications are presented in θ-chainable space and ordered metric space.
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