Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 592504, 10 pages
doi:10.1155/2008/592504
Research Article

Additive Functional Inequalities in Banach Modules

Choonkil Park,1 Jong Su An,2 and Fridoun Moradlou3

1Department of Mathematics, Hanyang University, Seoul 133–791, South Korea
2Department of Mathematics Education, Pusan National University, Pusan 609–735, South Korea
3Faculty of Mathematical Science, University of Tabriz, Tabriz 5166 15731, Iran

Received 1 April 2008; Revised 4 June 2008; Accepted 10 November 2008

Academic Editor: Alberto Cabada

Copyright © 2008 Choonkil Park et al. 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 investigate the following functional inequality ‖2f(x)+2f(y)+2f(z)−f(x+y)−f(y+z)‖≤‖f(x+z)‖ in Banach modules over a C∗-algebra and prove the generalized Hyers-Ulam stability of linear mappings in Banach modules over a C∗-algebra in the spirit of the Th. M. Rassias stability approach. Moreover, these results are applied to investigate homomorphisms in complex Banach algebras and prove the generalized Hyers-Ulam stability of homomorphisms in complex Banach algebras.