Fixed points and hyers-ulam-rassias stability of cauchy-jensen functional equations in banach algebras

Abstract

We prove the Hyers-Ulam-Rassias stability of homomorphisms in real Banach algebras and of generalized derivations on real Banach algebras for the following Cauchy-Jensen functional equations: f ( x + y/ 2+ z) + f ( x - y/ 2+ z) = f ( x) + 2f ( z), 2 f ( x + y/ 2+ z) = f ( x) + f ( y) + 2f ( z), which were introduced and investigated by Baak ( 2006). The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper (1978).