Hyers-Ulam stability of Jensen functional equation on amenable   semigroups
  In this paper, we give a proof of the Hyers-Ulam stability of the Jensen functional equation $$f(xy)+f(x\sigma(y))=2f(x),\phantom{+} x,y\in{G},$$ where $G$ is an amenable semigroup and $\sigma$ is an involution of $G.$ 
Bouikhalene Belaid and Elqorachi Elhoucien
math.FA