STABILITY OF THE JENSEN TYPE FUNCTIONAL EQUATION IN BANACH ALGEBRAS: A FIXED POINT APPROACH

Abstract

Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in Banach algebras and of derivations on Banach algebras for the following Jensen type functional equation:

$$f(\frac{x+y}{2})+f(\frac{x-y}{2})=f(x)$$