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MODULE EXTENSION OF DUAL BANACH ALGEBRAS
Gordji, Madjid Eshaghi,Habibian, Fereydoun,Rejali, Ali Korean Mathematical Society 2010 대한수학회보 Vol.47 No.4
This work was intended as an attempt to introduce and investigate the Connes-amenability of module extension of dual Banach algebras. It is natural to try to study the $weak^*$-continuous derivations on the module extension of dual Banach algebras and also the weak Connes-amenability of such Banach algebras.
Generalized Ulam-Hyers Stability of Jensen Functional Equation in Šerstnev PN Spaces
Gordji, M. Eshaghi,Ghaemi, M. B.,Majani, H.,Park, C. Hindawi Publishing Corporation 2010 Journal of inequalities and applications Vol.2010 No.1
<P>We establish a generalized Ulam-Hyers stability theorem in a Šerstnev probabilistic normed space (briefly, Šerstnev PN-space) endowed with ΠM. In particular, we introduce the notion of approximate Jensen mapping in PN-spaces and prove that if an approximate Jensen mapping in a Šerstnev PN-space is continuous at a point then we can approximate it by an everywhere continuous Jensen mapping. As a version of a theorem of Schwaiger, we also show that if every approximate Jensen type mapping from the natural numbers into a Šerstnev PN-space can be approximated by an additive mapping, then the norm of Šerstnev PN-space is complete.</P>
APPROXIMATION OF CUBIC MAPPINGS WITH n-VARIABLES IN β-NORMED LEFT BANACH MODULE ON BANACH ALGEBRAS
Gordji, Majid Eshaghi,Khodaei, Hamid,Najati, Abbas Korean Mathematical Society 2011 대한수학회보 Vol.48 No.5
Let M = {1, 2, ${\ldots}$, n} and let V = {$I{\subseteq}M:1{\in}I$}. Denote M\I by $I^c$ for $I{\in}V$. The goal of this paper is to investigate the solution and the stability using the alternative fixed point of generalized cubic functional equation $ \sum\limits_{I{\in}V}f(\sum\limits_{i{\in}I}a_ix_i-\sum\limits_{i{\in}I^c}a_ix_i)=2{^{n-2}{a_1}}\sum\limits_{i=2}^na_i^2[f(x_1+x_i)+f(x_1-x_i)]+2{^{n-1}{a_1}(a^2_1-\sum\limits_{i=2}^2a^2_i)f(x_1)$ in ${\beta}$-Banach modules on Banach algebras, where $a_1,{\ldots},a_n{\in}\mathbb{Z}{\backslash}\{0\}$ with $a_1{\neq}={\pm}1$ and $a_n=1$.
JORDAN *-HOMOMORPHISMS BETWEEN UNITAL C<sup>*</sup>-ALGEBRAS
Gordji, Madjid Eshaghi,Ghobadipour, Norooz,Park, Choon-Kil Korean Mathematical Society 2012 대한수학회논문집 Vol.27 No.1
In this paper, we prove the superstability and the generalized Hyers-Ulam stability of Jordan *-homomorphisms between unital $C^*$-algebras associated with the following functional equation$$f(\frac{-x+y}{3})+f(\frac{x-3z}{c})+f(\frac{3x-y+3z}{3})=f(x)$$. Morever, we investigate Jordan *-homomorphisms between unital $C^*$-algebras associated with the following functional inequality $${\parallel}f(\frac{-x+y}{3})+f(\frac{x-3z}{3})+f(\frac{3x-y+3z}{3}){\parallel}\leq{\parallel}f(x)\parallel$$.
ON A COMPOSITE FUNCTIONAL EQUATION RELATED TO THE GOLAB-SCHINZEL EQUATION
Gordji, Madjid Eshaghi,Rassias, Themistocles M.,Tial, Mohamed,Zeglami, Driss Korean Mathematical Society 2016 대한수학회보 Vol.53 No.2
Let X be a vector space over a field K of real or complex numbers and $k{\in}{\mathbb{N}}$. We prove the superstability of the following generalized Golab-Schinzel type equation $f(x_1+{\limits\sum_{i=2}^p}x_if(x_1)^kf(x_2)^k{\cdots}f(x_{i-1})^k)={\limits\prod_{i=1}^pf(x_i),x_1,x_2,{\cdots},x_p{\in}X$, where $f:X{\rightarrow}K$ is an unknown function which is hemicontinuous at the origin.
Coupled Fixed-Point Theorems for Contractions in Partially Ordered Metric Spaces and Applications
Gordji, M. Eshaghi,Cho, Y. J.,Ghods, S.,Ghods, M.,Dehkordi, M. Hadian Hindawi Limited 2012 Mathematical problems in engineering Vol.2012 No.-
<P>Bhaskar and Lakshmikantham (2006) showed the existence of coupled coincidence points of a mappingFfromX×XintoXand a mappinggfromXintoXwith some applications. The aim of this paper is to extend the results of Bhaskar and Lakshmikantham and improve the recent fixed-point theorems due to Bessem Samet (2010). Indeed, we introduce the definition of generalizedg-Meir-Keeler type contractions and prove some coupled fixed point theorems under a generalizedg-Meir-Keeler-contractive condition. Also, some applications of the main results in this paper are given.</P>
STABILITY OF A FUNCTIONAL EQUATION DERIVING FROM QUARTIC AND ADDITIVE FUNCTIONS
Gordji, Madjid Eshaghi Korean Mathematical Society 2010 대한수학회보 Vol.47 No.3
In this paper, we obtain the general solution and the generalized Hyers-Ulam Rassias stability of the functional equation f(2x + y) + f(2x - y) = 4(f(x + y) + f(x - y)) - $\frac{3}{7}$(f(2y) - 2f(y)) + 2f(2x) - 8f(x).
SOME CHARACTERIZATIONS OF CHARACTER AMENABLE BANACH ALGEBRAS
Gordji, Madjid Eshaghi,Jabbari, Ali,Kim, Gwang Hui Korean Mathematical Society 2015 대한수학회보 Vol.52 No.3
In this study, the character amenability of Banach algebras is considered and some characterization theorems are established. Indeed, we prove that the character amenability of Lipschitz algebras is equivalent to that of Banach algebras.