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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 $a_n=1$.
Approximation of cubic mappings with n-variables in β-normed left Banach modules on Banach algebras
Majid Eshaghi Gordji,Hamid Khodaei,Abbas Najati 대한수학회 2011 대한수학회보 Vol.48 No.5
Let M={1,2,...,n,} and let V={I⊆ M: 1∈ I}. Denote M\I by I^c for I∈V. The goal of this paper is to investigate the solution and the stability using the alternative fixed point of generalized cubic functional equation [수식]=[수식] in β-Banach modules on Banach algebras, where a_1,...,a_n ∈Z\{0} with a_1≠±1 and a_n=1.
Some Ćiric Type Fixed Point Results in non-Archimedean Modular Metric Spaces
HODA HOSSEINI,Majid Eshaghi Gordji 한국수학교육학회 2019 純粹 및 應用數學 Vol.26 No.4
In this paper, we establish some Ciric type fixed point theorems in α−complete and orbitally T−complete non-Archimedean modular metric spaces. Meanwhile, we present an illustrative example to emphasis the realized improvements. These obtained results extend and improve certain well known results in the literature
APPROXIMATELY QUINTIC AND SEXTIC MAPPINGS ON THE PROBABILISTIC NORMED SPACES
Ghaemi, Mohammad Bagher,Majani, Hamid,Gordji, Majid Eshaghi Korean Mathematical Society 2012 대한수학회보 Vol.49 No.2
We prove the stability for the systems of quadratic-cubic and additive-quadratic-cubic functional equations with constant coefficients on the probabilistic normed spaces (briefly PN spaces).
APPROXIMATELY QUINTIC AND SEXTIC MAPPINGS ON THE PROBABILISTIC NORMED SPACES
Mohammad Bagher Ghaemi,Hamid Majani,Majid Eshaghi Gordji 대한수학회 2012 대한수학회보 Vol.49 No.2
We prove the stability for the systems of quadratic-cubic and additive-quadratic-cubic functional equations with constant coefficients on the probabilistic normed spaces (briefly PN spaces).