


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:
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:
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:
Pseudomonotonicity and Quasimonotonicity by Translations versus Monotonicity in Hilbert Spaces
Author(s):
George Isac and Dumitru Motreanu
Department of
Mathematics, Royal Military College of Canada, P.O. Box 17000 Stn Forces
Kingston, Ontario, Canada, K7k 7b4.
gisac@juno.com
Département de Mathématiques, Université de Perpignan, 66860
Perpignan, France.
motreanu@univperp.fr
Abstract:
Let _{ }be a Gâteaux differentiable mapping on an open convex subset _{ }of a Hilbert space_{}. If there exists a straight line _{ }such that _{ }is pseudomonotone for any _{ }then _{ }is monotone. Related results using a regularity condition are given.
Paper's Title:
A Fixed Point Approach to
the Stability of the Equation
Author(s):
SoonMo Jung
Mathematics Section, College of Science and Technology
HongIk
University, 339701 Chochiwon
Republic of Korea.
smjung@hongik.ac.kr
Abstract:
We will apply a fixed point method for proving the HyersUlam stability of the functional equation .
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:
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:
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:
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:
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:
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:
Differentiability of Distance Functions in pNormed Spaces
Author(s):
M. S. Moslehian, A. Niknam, S. Shadkam Torbati
Department of Pure Mathematics,
Centre of Excellence in Analysis on Algebraic Structures (CEAAS),,
Ferdowsi University of Mashhad,
P. O. Box
1159, Mashhad,
Iran
moslehian@ferdowsi.um.ac.ir
niknam@math.um.ac.ir
shadkam.s@wali.um.ac.ir
Abstract:
The farthest point mapping in a pnormed space X is studied in virtue of the Gateaux derivative and the Frechet derivative. Let M be a closed bounded subset of X having the uniformly pGateaux differentiable norm. Under certain conditions, it is shown that every maximizing sequence is convergent, moreover, if M is a uniquely remotal set then the farthest point mapping is continuous and so M is singleton. In addition, a HahnBanach type theorem in $p$normed spaces is proved.
Paper's Title:
Stability of a Pexiderized Equation
Author(s):
Maryam Amyar
Department of Mathematics,
Islamic Azad University, Rahnamaei Ave,
Mashhad 91735, Iran,
and Banach Mathematical Research Group (BMRG)
amyari@mshdiau.ac.ir
URL: http://amyari.mshdiau.ac.ir
Abstract:
The aim of the paper is to prove the stability of the Pexiderized equation f(x)=g(y+x)h(yx), for any amenable abelian group.
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:
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:
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:
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:
Ulam Stability of Reciprocal Difference and Adjoint Functional Equations
Author(s):
K. Ravi, J. M. Rassias and B. V. Senthil Kumar
Department of Mathematics,
Sacred Heart College, Tirupattur  635601,
India
Pedagogical Department E. E.,
Section of Mathematics and Informatics,
National and Capodistrian University of Athens,
4, Agamemnonos Str., Aghia Paraskevi,
Athens, Attikis 15342,
GREECE
Department of Mathematics,
C.Abdul Hakeem College of Engineering and
Technology, Melvisharam  632 509, India
shckavi@yahoo.co.in
jrassias@primedu.uoa.gr
bvssree@yahoo.co.in
Abstract:
In this paper, the reciprocal difference functional equation (or RDF equation) and the reciprocal adjoint functional equation (or RAF equation) are introduced. Then the pertinent Ulam stability problem for these functional equations is solved, together with the extended Ulam (or Rassias) stability problem and the generalized Ulam (or UlamGavrutaRassias) stability problem for the same equations.
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