Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 904852, 8 pages
doi:10.1155/2008/904852
Research Article
On the Cauchy Functional Inequality in Banach Modules
Department of Mathematics, Hanyang University, Seoul 133791, South Korea
Received 17 January 2008; Revised 21 March 2008; Accepted 16 April 2008
Academic Editor: Ram Mohapatra
Copyright © 2008 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 investigate the following functional inequality: ‖f(x)+f(y)+f(z)‖≤‖f(x+y+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.