Hyers-Ulam-Rassias stability of a generalized Pexider functional equation

Abstract

In this paper, we obtain the Hyers-Ulam-Rassias stability of the generalized Pexider functional equation $$ \sum_{k\in K} f(x+k\cdot y)=|K|g(x)+|K|h(y), \; x, y \in G ,$$ where $G$ is an abelian group, $K$ is a finite abelian subgroup of the group of automorphism of $G$.

The concept of Hyers-Ulam-Rassias stability originated from Th.M. Rassias' Stability Theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72(1978), 297-300.