Fixed Points and Stability for Quadratic Mappings in β–Normed Left Banach Modules on Banach Algebras

被引:0
作者
M. Eshaghi. Gordji
H. Khodaei
Th. M. Rassias
机构
[1] Semnan University,Department of Mathematics
[2] Semnan University,Center of Excellence in Nonlinear Analysis and Applications (CENAA)
[3] National Technical University of Athens,Department of Mathematics
来源
Results in Mathematics | 2012年 / 61卷
关键词
Primary 47H10; Secondary 39B82; 39B52; 46H25; Generalized Hyers–Ulam stability; quadratic functional equation; Banach module; unital Banach algebra; generalized metricspace; fixed point method;
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摘要
The goal of the present paper is to investigate some new stability results by applying the alternative fixed point of generalized quadratic functional equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{array}{ll}f\left(\sum\limits_{i=1}^{n}a_ix_i\right)+{\sum\limits_{i=1}^{n-1}}{\sum\limits_{j=i+1}^{n}}\left[f(a_ix_i+a_jx_j)+2f(a_ix_i-a_jx_j)\right]\\ \qquad \quad = (3n-2){\sum\limits_{i=1}^{n}}a^2_{i}f(x_{i})\end{array}$$\end{document}in β–Banach modules on Banach algebras, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${a_{1},\dots,a_{n}\in \mathbb{Z}{\setminus}\{0\}}$$\end{document} and some \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\ell\in\{1 , 2 ,\dots, n-1\},}$$\end{document}aℓ ≠ ±1 and an = 1, where n is a positive integer greater or at least equal to two.
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页码:393 / 400
页数:7
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