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

Recommended by Ram Verma

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.