Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 298050, 8 pages
doi:10.1155/2008/298050
Research Article
Fixed Points in Functional Inequalities
Department of Mathematics, Hanyang University, Seoul 133791, South Korea
Received 29 September 2008; Accepted 16 December 2008
Academic Editor: Shusen Ding
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
Using fixed point methods, we prove the generalized Hyers-Ulam stability
of the following functional inequalities ‖f(x)+f(y)+f(z)‖≤‖f(x+y+z)‖ and ‖f(x)+f(y)+2f(z)‖≤‖2f((x+y)/2+z)‖ in the spirit of Th. M. Rassias stability approach.