Advances in Difference Equations
Volume 2009 (2009), Article ID 973709, 14 pages
doi:10.1155/2009/973709
Research Article

A Functional Inequality in Restricted Domains of Banach Modules

M. B. Moghimi,1 Abbas Najati,1 and Choonkil Park2

1Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199–11367, Iran
2Department of Mathematics, Hanyang University, Seoul 133-791, South Korea

Received 28 April 2009; Revised 2 August 2009; Accepted 16 August 2009

Academic Editor: Binggen Zhang

Copyright © 2009 M. B. Moghimi 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 stability problem for the following functional inequality ∥αf((x+y)/2α)+βf((y+z)/2β)+γf((z+x)/2γ)∥≤∥f(x+y+z)∥ on restricted domains of Banach modules over a C∗-algebra. As an application we study the asymptotic behavior of a generalized additive mapping.