Generalized Hyers-Ulam Stability for General Additive Functional Equations on Non-Archimedean Random Lie C* -Algebras

Abstract

In this paper, using the fixed point method, we prove some results related to the generalized Hyers-Ulam stability of homomorphisms and derivations in non-Archimedean random $C^{\ast}$-algebras and non-Archimedean random Lie $C^{\ast}$-algebras for the generalized additive functional equation

\begin{eqnarray*}

\sum_{1\leq i< j\leq

n}f\bigg (\frac{x_{i} +x_{j}}{2}\,\, +\sum^{n-2}_{l =1,\,\, k_{l}\neq

i,j} x_{{k_{}}_{l}} \bigg )=\frac{(n-1)^{2}}{2}\, \sum^{n}_{i=1}f(x_{i})

\end{eqnarray*}

where $n\in {\mathbb{N}}$ is a fixed integer with $n\geq 3$.