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STABILITY OF A FUNCTIONAL EQUATION DERIVING FROM QUARTIC AND ADDITIVE FUNCTIONS
Madjid Eshaghi Gordji 대한수학회 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)) −37(f(2y) − 2f(y)) + 2f(2x) − 8f(x).
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.
SOME CHARACTERIZATIONS OF CHARACTER AMENABLE BANACH ALGEBRAS
Madjid Eshaghi Gordji,Ali Jabbari,김광휘 대한수학회 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.
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).
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 $${\parallel}f(\frac{-x+y}{3})+f(\frac{x-3z}{3})+f(\frac{3x-y+3z}{3}){\parallel}\leq{\parallel}f(x)\parallel$$.
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.
On a composite functional equation related to the Golab-Schinzel equation
Madjid Eshaghi Gordji,Themistocles M. Rassias,Mohamed Tial,Driss Zeglami 대한수학회 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 \begin{equation*} f(x_{1}+\sum_{i=2}^{p}x_{i}f(x_{1})^{k} f(x_{2})^{k}\cdots f(x_{i-1})^{k})=\prod \limits_{i=1}^{p}f(x_{i}),\ x_{1},x_{2},\ldots,x_{p}\in X, \end{equation*} where $f:X\rightarrow K$ is an unknown function which is hemicontinuous at the origin.