Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 403101, 16 pages
doi:10.1155/2010/403101
Research Article

Solutions and Stability of Generalized Mixed Type QC Functional Equations in Random Normed Spaces

Yeol Je Cho,1 Madjid Eshaghi Gordji,2 and Somaye Zolfaghari3

1Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Republic of Korea
2Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran
3Department of Mathematics, Urmia University, Urmia, Iran

Received 29 July 2010; Accepted 31 August 2010

Academic Editor: Vijay Gupta

Copyright © 2010 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 achieve the general solution and the generalized stability result for the following functional equation in random normed spaces (in the sense of Sherstnev) under arbitrary t-norms: f(x+ky)+f(x−ky)=k2[f(x+y)+f(x−y)]+(2(k2−1)/k2(k−2))f(kx)−((k3−k2−k+1)/2(k−2))f(2x)+f˜(2y)−8f˜(y), where f˜(y):=f(y)−f(−y) for any fixed integer k with k≠0,  ±1,2.