Hyers-Ulam stability of Jensen functional equation on amenable semigroups

Abstract

In this paper, we give a proof of the Hyers-Ulam stability of the Jensen functional equation $$f(xy)+f(x\sigma (y))=2f(x),x,y\in G,$$ where $G$ is an amenable semigroup and $\sigma$ is an involution of $G.$

7 pages