


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:
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:
Stability of a Mixed Additive, Quadratic and Cubic Functional Equation In QuasiBanach Spaces
Author(s):
A. Najati and F. Moradlou
Department of Mathematics, Faculty of Sciences,
University of Mohaghegh Ardabili, Ardabil,
Iran
a.nejati@yahoo.com
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz,
Iran
moradlou@tabrizu.ac.ir
Abstract:
In this paper we establish the general solution of a mixed additive, quadratic and cubic functional equation and investigate the HyersUlamRassias stability of this equation in quasiBanach spaces. The concept of HyersUlamRassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297300.
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:
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 the Ulam Stability for EulerLagrange Type Quadratic Functional Equations
Author(s):
Matina John Rassias and John Michael Rassias
Statistics and Modelling Science,
University of Strathclyde,
Livingstone Tower,
26 Richmond Str,
Glasgow, Uk, G1 1xh
Pedagogical Department, E. E., National and Capodistrian University of Athens,
Section of Mathematics and Informatics,
4, Agamemnonos Str, Aghia Paraskevi,
Athens 15342, Greece
Abstract:
In 1940 (and 1968) S. M. Ulam proposed the wellknown Ulam stability problem. In 1941 D.H. Hyers solved the HyersUlam problem for linear mappings. In 1951 D. G. Bourgin has been the second author treating the Ulam problem for additive mappings. In 1978 according to P.M. Gruber this kind of stability problems is of particular interest in probability theory and in the case of functional equations of different types. In 19822004 we established the HyersUlam stability for the Ulam problem for different mappings. In 19922000 J.M. Rassias investigated the Ulam stability for EulerLagrange mappings. In this article we solve the Ulam problem for EulerLagrange type quadratic functional equations. These stability results can be applied in mathematical statistics, stochastic analysis, algebra, geometry, as well as in psychology and sociology.
Paper's Title:
Solution of the HyersUlam Stability Problem for Quadratic Type Functional Equations in Several Variables
Author(s):
John Michael Rassias
Pedagogical Department, E.E., National and Capodistrian University of Athens,
Section of Mathematics and Informatics,
4, Agamemnonos Str., Aghia Paraskevi,
Athens 15342,
Greece
jrassias@primedu.uoa.gr
URL: http://www.primedu.uoa.gr/~jrassias/
Abstract:
In 1940 (and 1968) S. M. Ulam proposed the wellknown Ulam stability problem. In 1941 D. H. Hyers solved the HyersUlam problem for linear mappings. In 1951 D. G. Bourgin has been the second author treating the Ulam problem for additive mappings. In 1978 according to P. M. Gruber this kind of stability problems is of particular interest in probability theory and in the case of functional equations of different types. In 19822004 we established the HyersUlam stability for the Ulam problem for different mappings. In this article we solve the HyersUlam problem for quadratic type functional equations in several variables. These stability results can be applied in stochastic analysis, financial and actuarial mathematics, as well as in psychology and sociology.
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:
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:
A New Relaxed bmetric Type and Fixed Point Results
Author(s):
P. Singh, V. Singh and Thokozani Cyprian Martin Jele
Department of Mathematics,
University of KwaZuluNatal,
Private Bag X54001, Durban,
South Africa.
Email: singhp@ukzn.ac.za,
singhv@ukzn.ac.za,
thokozani.jele@nwu.ac.za
Abstract:
The purpose of this paper is to introduce a new relaxed α, β bmetric type by relaxing the triangle inequality. We investigate the effect that this generalization has on fixed point theorems.
Paper's Title:
Existence of Solution of Differential and RiemannLiouville Equation Via Fixed Point Approach in Complex Valued bMetric 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.
Email: komia@aims.ac.za
DSTNRF Centre of Excellence in
Mathematical and Statistical Sciences (CoEMaSS),
Johannesburg,
South Africa.
Email: dele@aims.ac.za
DSTNRF Centre of Excellence in
Mathematical and Statistical Sciences (CoEMaSS),
Johannesburg,
South Africa.
Email: hammedabass548@gmail.com
School of Mathematics, Statistics and
Computer Science,
University of KwaZuluNatal, Durban,
South Africa.
Email: 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 Cclass function in the framework of complex valued bmetric spaces. As an application, we establish the existence and uniqueness of a solution for RiemannLiouville integral and ordinary differential equation in the framework of a complete complex valued bmetric spaces. The obtained results generalize and improve some fixed point results in the literature.
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:
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:
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 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:
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:
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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