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

Choonkil Park,1 Young Sun Cho,2 and Mi-Hyen Han2

 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

Recommended by Sever S. Dragomir

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.