Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 153084, 26 pages
doi:10.1155/2009/153084
Research Article

On the Stability of a Generalized Quadratic and Quartic Type Functional Equation in Quasi-Banach Spaces

M. Eshaghi Gordji,1 S. Abbaszadeh,1 and Choonkil Park2

1Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran
2Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, South Korea

Received 31 May 2009; Accepted 9 September 2009

Academic Editor: Nikolaos Papageorgiou

Copyright © 2009 M. Eshaghi Gordji 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

We establish the general solution of the functional equation f(nx+y)+f(nx−y)=n2f(x+y)+n2f(x−y)+2(f(nx)−n2f(x))−2(n2−1)f(y) for fixed integers n with n≠0,±1 and investigate the generalized Hyers-Ulam stability of this equation in quasi-Banach spaces.