Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 872190, 11 pages
doi:10.1155/2008/872190
Research Article

Stability of the Cauchy-Jensen Functional Equation in C∗-Algebras: A Fixed Point Approach

Choonkil Park1 and Jong Su An2

1Department of Mathematics, Hanyang University, Seoul 133-791, South Korea
2Department of Mathematics Education, Pusan National University, Pusan 609-735, South Korea

Received 3 April 2008; Accepted 14 May 2008

Academic Editor: Andrzej Szulkin

Copyright © 2008 Choonkil Park and Jong Su An. 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 C∗-algebra homomorphisms and of generalized derivations on C∗-algebras for the following Cauchy-Jensen functional equation 2f((x+y)/2+z)=f(x)+f(y)+2f(z), which was introduced and investigated by Baak (2006). The concept of Hyers-Ulam-Rassias stability originated from the stability theorem of Th. M. Rassias that appeared in (1978).