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Park, C.,Lee, J.R.,Shin, D.Y.,Gordji, M.E. World Scientific 2013 International journal of geometric methods in mode Vol.10 No.2
<P>Eshaghi Gordji and Ghobadipour proved the Hyers-Ulam stability of (alpha, beta, gamma)derivations on Lie C*-algebras associated with the following functional equation f(x(2) - x(1)/3) + f(x(1) - 3x(3)/3) + f(3x(1) + 3x(3) - x(2)/3) = f(x(1)). Under the conditions in the main theorems, we can show that the related mappings must be zero. In this paper, we correct the conditions and prove the corrected theorems.</P>
Approximate Quartic and Quadratic Mappings in Quasi-Banach Spaces
Gordji, M. Eshaghi,Khodaei, H.,Kim, Hark-Mahn Hindawi Publishing Corporation 2011 International journal of mathematics and mathemati Vol.2011 No.-
<P>we establish the general solution for a mixed type functional equation of aquartic and a quadratic mapping in linear spaces. In addition, we investigate the generalized Hyers-Ulam stability in p-Banach spaces.</P>
Hyers-Ulam Stability of a Tribonacci Functional Equation in 2-Normed Spaces
Gordji, M.E.,Divandari, A.,Rostamian, M.,Park, C.,Shin, D.Y. Eudoxus Press LLC 2014 Journal of computational analysis and applications Vol.16 No.3
In this paper, we investigate the Hyers-Ulam stability of the Tribonacci functional equationf(x) = f(x - 1) + f(x - 2) + f(x - 3)in 2-Banach spaces.
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>
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.
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 $${\parallel}f(\frac{-x+y}{3})+f(\frac{x-3z}{3})+f(\frac{3x-y+3z}{3}){\parallel}\leq{\parallel}f(x)\parallel$$.
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 $a_n=1$.
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.