Journal of Applied Mathematics
Volume 2012 (2012), Article ID 902931, 45 pages
http://dx.doi.org/10.1155/2012/902931
Review Article

Nonlinear Random Stability via Fixed-Point Method

Yeol Je Cho,1 Shin Min Kang,2 and Reza Saadati3

1Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Republic of Korea
2Department of Mathematics and the RINS, Gyeongsang National University, Chinju 660-701, Republic of Korea
3Department of Mathematics, Iran University of Science and Technology, Behshahr, Iran

Received 31 October 2011; Accepted 22 December 2011

Academic Editor: Yeong-Cheng Liou

Copyright © 2012 Yeol Je Cho 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 prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equation 𝑓 ( 𝑥 + 2 𝑦 ) + 𝑓 ( 𝑥 − 2 𝑦 ) = 4 𝑓 ( 𝑥 + 𝑦 ) + 4 𝑓 ( 𝑥 − 𝑦 ) − 6 𝑓 ( 𝑥 ) + 𝑓 ( 2 𝑦 ) + 𝑓 ( − 2 𝑦 ) − 4 𝑓 ( 𝑦 ) − 4 𝑓 ( − 𝑦 ) in various complete random normed spaces.