Hyers-Ulam-Rassias Approximation on Lie Algebras

Abstract

Using the fixed point method, we establish the stability of $m-$Lie homomorphisms and Jordan $m-$Lie homomorphisms on $m-$Lie algebras  associated to the  followingadditive functional equation $$2\mu f\left(\sum_{i=1}^m  m x_i\right)=\sum_{i=1}^mf\left(\mu  \left(m x_i + \sum_{j=1~,i\neq j}^m x_j\right)\right)+f\left(\sum_{i=1}^m \mu x_i\right)$$where $m$ be an integer greater than 2 and all $\mu\in  \Bbb T_{\frac{1}{n_0}} :=\left\{e^{i\theta} \ ;\0\leq\theta\leq \frac{2\pi}{n_0}\right\}$.