Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 185780, 16 pages
doi:10.1155/2010/185780
Research Article

A Fixed Point Approach to the Stability of an Additive-Quadratic-Cubic-Quartic Functional Equation

Jung Rye Lee,1 Ji-hye Kim,2 and Choonkil Park2

1Department of Mathematics, Daejin University, Kyeonggi 487-711, South Korea
2Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, South Korea

Received 24 August 2009; Revised 16 November 2009; Accepted 10 January 2010

Academic Editor: Fabio Zanolin

Copyright © 2010 Jung Rye Lee 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

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equation f(x+2y)+f(x−2y)=4f(x+y)+4f(x−y)−6f(x)+f(2y)+f(−2y)−4f(y)−4f(−y) in Banach spaces.