Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 210626, 13 pages
doi:10.1155/2008/210626
Research Article

On the Stability of Generalized Additive Functional Inequalities in Banach Spaces

Jung Rye Lee,1 Choonkil Park,2 and Dong Yun Shin3

1Department of Mathematics, Daejin University, Kyeonggi 487-711, South Korea
2Department of Mathematics, Hanyang University, Seoul 133-791, South Korea
3Department of Mathematics, University of Seoul, Seoul 130-743, South Korea

Received 18 February 2008; Accepted 2 May 2008

Academic Editor: Ram Verma

Copyright © 2008 Jung Rye Lee 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 study the following generalized additive functional inequality ‖af(x)+bf(y)+cf(z)‖≤‖f(αx+βy+γz)‖, associated with linear mappings in Banach spaces. Moreover, we prove the Hyers-Ulam-Rassias stability of the above generalized additive functional inequality, associated with linear mappings in Banach spaces.