Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 41820, 13 pages
doi:10.1155/2007/41820
Research Article
Functional Inequalities Associated with Jordan‐von Neumann‐Type Additive Functional Equations
1Department of Mathematics, Hanyang University, Seoul 133‐791, South Korea
2Department of Mathematics, Chungnam National University, Daejeon 305‐764, South Korea
Received 27 September 2006; Accepted 1 November 2006
Academic Editor: Sever S. Dragomir
Copyright © 2007 Choonkil Park 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 prove the generalized Hyers‐Ulam stability of the following functional inequalities: ||f(x)+f(y)+f(z)|| ≤ ||2f((x+y+z)/2)||, ||f(x)+f(y)+f(z)|| ≤ ||f(x+y+z)||, ||f(x)+f(y)+2f(z)|| ≤ ||2f((x+y)/2+z)|| in the spirit of the Rassias stability approach for approximately homomorphisms.