Abstract and Applied Analysis
Volume 2011 (2011), Article ID 463164, 18 pages
http://dx.doi.org/10.1155/2011/463164
Research Article

General Cubic-Quartic Functional Equation

M. Eshaghi Gordji,1,2 M. Kamyar,1,2 and Th. M. Rassias3

1Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran
2Center of Excellence in Nonlinear Analysis and Applications (CENAA), Semnan University, Semnan, Iran
3Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece

Received 25 June 2011; Accepted 22 August 2011

Academic Editor: Victor M. Perez Garcia

Copyright © 2011 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 obtain the general solution and the generalized Hyers-Ulam stability of the general cubic-quartic functional equation for fixed integers k with 𝑘 ≠ 0 , ± 1 : 𝑓 ( 𝑥 + 𝑘 𝑦 ) + 𝑓 ( 𝑥 − 𝑘 𝑦 ) = 𝑘 2 ( 𝑓 ( 𝑥 + 𝑦 ) + 𝑓 ( 𝑥 − 𝑦 ) ) + 2 ( 1 − 𝑘 2 ) 𝑓 ( 𝑥 ) + ( ( 𝑘 4 − 𝑘 2 ) / 4 ) ( 𝑓 ( 2 𝑦 ) − 8 𝑓 ( 𝑦 ) ) + 𝑓 ( 2 𝑥 ) − 1 6 𝑓 ( 𝑥 ) , where 𝑓 ( 𝑥 ) ∶ = 𝑓 ( 𝑥 ) + 𝑓 ( − 𝑥 ) .