Journal of Inequalities and Applications
Volume 2011 (2011), Article ID 194394, 23 pages
doi:10.1155/2011/194394
Review Article

Nonlinear ℒ -Random Stability of an ACQ Functional Equation

Reza Saadati, M. M. Zohdi, and S. M. Vaezpour

Department of Mathematics, Science and Research Branch, Islamic Azad University, Ashrafi Esfahani Ave, Tehran 14778, Iran

Received 9 December 2010; Accepted 6 February 2011

Academic Editor: Soo Hak Sung

Copyright © 2011 Reza Saadati 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-cubic-quartic functional equation: 1 1 𝑓 ( 𝑥 + 2 𝑦 ) + 1 1 𝑓 ( 𝑥 − 2 𝑦 ) = 4 4 𝑓 ( 𝑥 + 𝑦 ) + 4 4 𝑓 ( 𝑥 − 𝑦 ) + 1 2 𝑓 ( 3 𝑦 ) − 4 8 𝑓 ( 2 𝑦 ) + 6 0 𝑓 ( 𝑦 ) − 6 6 𝑓 ( 𝑥 ) in complete latticetic random normed spaces.