Approximation of a generalized Euler-Lagrange type additive mapping on Lie $C^{\ast}$-algebras

	Approximation of a generalized Euler-Lagrange type additive mapping on Lie $C^{\ast}$-algebras
International Journal of Nonlinear Analysis and Applications
مقاله 17، دوره 7، شماره 2، 2016، صفحه 195-204 اصل مقاله (395.95 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2017.1332.1329
نویسندگان
Zhihua Wang^* ¹؛ Prasanna K. Sahoo²
¹School of Science, Hubei University of Technology, Wuhan, Hubei 430068, P.R. China
²Department of Mathematics, University of Louisville, Louisville, KY 40292, USA
چکیده
Using fixed point method, we prove some new stability results for Lie $(\alpha,\beta,\gamma)$-derivations and Lie $C^{\ast}$-algebra homomorphisms on Lie $C^{\ast}$-algebras associated with the Euler-Lagrange type additive functional equation \begin{align} \sum^{n}_{j=1}f{\bigg(-r_{j}x_{j}+\sum_{1\leq i \leq n, i\neq j}r_{i}x_{i}\bigg)}+2\sum^{n}_{i=1}r_{i}f(x_{i})=nf{\bigg(\sum^{n}_{i=1}r_{i}x_{i}\bigg)} \end{align} where $r_{1},\ldots,r_{n}\in {\mathbb{R}}$ are given and $r_{i},r_{j}\neq 0$ for some $1\leq i< j\leq n$.
کلیدواژه‌ها
Fixed point theorem؛ Lie $(alpha,beta,gamma)$-derivation؛ Lie $C^{ast}$-algebra homomorphisms؛ generalized Hyers-Ulam stability
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