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Abstract and Applied Analysis
Volume 2007, Article ID 35151, 15 pages
Research Article

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

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

Academic Editor: John Michael Rassias

Copyright © 2007 Kil-Woung Jun 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.


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.