Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 754210, 18 pages
doi:10.1155/2010/754210
Research Article

Random Stability of an Additive-Quadratic-Quartic Functional Equation

M. Mohamadi,1 Y. J. Cho,2 C. Park,3 P. Vetro,4 and R. Saadati5

1Department of Mathematics, Islamic Azad University-Ayatollah Amoli Branch, Amol, P.O. Box 678, Iran
2Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, South Korea
3Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, South Korea
4Dipartimento di Matematica ed Applicazioni, Università degli Studi di Palermo, Via Archirafi, 34 - 90123 Palermo, Italy
5Faculty of Sciences, Islamic Azad University-Ayatollah Amoli Branch, Amol, P.O. Box 678, Iran

Received 7 December 2009; Accepted 8 February 2010

Academic Editor: Jong Kim

Copyright © 2010 M. Mohamadi 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-quartic functional equation f(x+2y)+f(x−2y)=2f(x+y)+2f(−x−y)+2f(x−y)+2f(y−x)−4f(−x)−2f(x)+f(2y)+f(−2y)−4f(y)−4f(−y) in complete random normed spaces.