Document Type : Research Paper

Authors

• Zhihua Wang ¹
• Prasanna K. Sahoo ²

¹ School of Science, Hubei University of Technology, Wuhan, Hubei 430068, P.R. China

² Department of Mathematics, University of Louisville, Louisville, KY 40292, USA

Abstract

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
$$\begin{array}{r}\sum _{j=1}^{n}f(-r_j{x}_j+\sum _{1\le i\le n,i\ne j}{r}_i{x}_i)+2\sum _{i=1}^n{r}_{i}f(x_i)=nf(\sum _{i=1}^n{r}_i{x}_i)\end{array}$$
where $r_1,\dots ,r_n\in \mathbb{R}$ are given and $r_i,r_j\ne 0$ for some $1\le i<j\le n$.

Keywords

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