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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 205160, 10 pages
http://dx.doi.org/10.1155/2012/205160
Research Article

A Fixed Point Approach to the Stability of a Cauchy-Jensen Functional Equation

1Graduate School of Education, Kyung Hee University, Yongin 446-701, Republic of Korea
2Department of Mathematics Education, College of Education, Mokwon University, Daejeon 302-729, Republic of Korea

Received 16 February 2012; Revised 6 April 2012; Accepted 20 April 2012

Academic Editor: Krzysztof Cieplinski

Copyright © 2012 Jae-Hyeong Bae and Won-Gil 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

We find out the general solution of a generalized Cauchy-Jensen functional equation and prove its stability. In fact, we investigate the existence of a Cauchy-Jensen mapping related to the generalized Cauchy-Jensen functional equation and prove its uniqueness. In the last section of this paper, we treat a fixed point approach to the stability of the Cauchy-Jensen functional equation.