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

Fixed Points and Hyers-Ulam-Rassias Stability of Cauchy-Jensen Functional Equations in Banach Algebras

Choonkil Park

Department of Mathematics, Hanyang University, Seoul 133-791, South Korea

Received 16 April 2007; Accepted 25 July 2007

Academic Editor: Billy E. Rhoades

Copyright © 2007 Choonkil Park. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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).