Abstract and Applied Analysis 
Volume 2007 (2007), Article ID 35151, 15 pages
doi:10.1155/2007/35151
Research Article

On the Generalized Hyers-Ulam Stability of a Cauchy-Jensen Functional Equation

Kil-Woung Jun,1,2 Yang-Hi Lee,3 and Young-Sun Cho2

1National Institute for Mathematical Sciences, Daejeon 305-340, South Korea
2Department of Mathematics, Chungnam National University, Daejeon 305-764, South Korea
3Department of Mathematics Education, Gongju National University of Education, Gongju 314-711, South Korea

Received 2 July 2007; Revised 27 August 2007; Accepted 22 October 2007

Recommended by John Michael Rassias

Abstract

In 2006, W. G. Park and J. H. Bae investigated the Hyers-Ulam stability of a Cauchy-Jensen functional equation. In this paper, we improve their results and obtain better results for a Cauchy-Jensen functional equation. Also, we establish new theorems for the generalized Hyers-Ulam stability of a Cauchy-Jensen functional equation.