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

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=۱}f{\bigg(-r_{j}x_{j}+\sum_{۱\leq i \leq n, i\neqj}r_{i}x_{i}\bigg)}+۲\sum^{n}_{i=۱}r_{i}f(x_{i})=nf{\bigg(\sum^{n}_{i=۱}r_{i}x_{i}\bigg)}\end{align*}where r_{۱},\ldots,r_{n}\in {\mathbb{R}} are given and r_{i},r_{j}\neq ۰ for some ۱\leq i< j\leq n.

کلیدواژه ها:

Fixed point theorem ، Lie (alpha ، beta ، gamma)-derivation ، Lie C^{ast}-algebra homomorphisms ، generalized Hyers-Ulam stability