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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

Choonkil Park

Department of Mathematics, Hanyang University, Seoul 133791, South Korea

Received 17 January 2008; Revised 21 March 2008; Accepted 16 April 2008

Recommended by Ram Mohapatra

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.