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http://dx.doi.org/10.4134/BKMS.2011.48.5.1063

APPROXIMATION OF CUBIC MAPPINGS WITH n-VARIABLES IN β-NORMED LEFT BANACH MODULE ON BANACH ALGEBRAS  

Gordji, Majid Eshaghi (Department of Mathematics Semnan University, Center of Excellence in Nonlinear Analysis and Applications (CENAA) Semnan University)
Khodaei, Hamid (Department of Mathematics Semnan University, Center of Excellence in Nonlinear Analysis and Applications (CENAA) Semnan University)
Najati, Abbas (Department of Mathematics University of Mohaghegh Ardabili)
Publication Information
Bulletin of the Korean Mathematical Society / v.48, no.5, 2011 , pp. 1063-1078 More about this Journal
Abstract
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 $a_n=1$.
Keywords
cubic functional equation; generalized Hyers-Ulam stability; Banach module;
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