Abstract and Applied Analysis
Volume 2009 (2009), Article ID 907167, 11 pages
doi:10.1155/2009/907167
Research Article

The Stability of a Quadratic Functional Equation with the Fixed Point Alternative

Choonkil Park1 and Ji-Hye Kim2

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

Received 15 September 2009; Accepted 1 December 2009

Academic Editor: W. A. Kirk

Copyright © 2009 Choonkil Park and Ji-Hye Kim. 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

Lee, An and Park introduced the quadratic functional equation f(2x+y)+f(2x−y)=8f(x)+2f(y) and proved the stability of the quadratic functional equation in the spirit of Hyers, Ulam and Th. M. Rassias. Using the fixed point method, we prove the generalized Hyers-Ulam stability of the quadratic functional equation in Banach spaces.