Fixed Point Theory and Applications
Volume 2007 (2007), Article ID 50175, 15 pages
doi:10.1155/2007/50175

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), 2f(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).