Abstract and Applied Analysis
Volume 2009 (2009), Article ID 923476, 11 pages
doi:10.1155/2009/923476
Research Article

On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations

M. Eshaghi Gordji and H. Khodaei

Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran

Received 17 December 2008; Revised 19 February 2009; Accepted 10 March 2009

Academic Editor: John Rassias

Copyright © 2009 M. Eshaghi Gordji and H. Khodaei. 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 achieve the general solution and the generalized Hyers-Ulam-Rassias and Ulam-Gavruta-Rassias stabilities for quadratic functional equations f(ax+by)+f(ax−by)=(b(a+b)/2)f(x+y)+(b(a+b)/2)f(x−y)+(2a2−ab−b2)f(x)+(b2−ab)f(y) where a, b are nonzero fixed integers with b≠±a,−3a, and f(ax+by)+f(ax−by)=2a2f(x)+2b2f(y) for fixed integers a, b with a,b≠0 and a±b≠0.