Advances in Difference Equations
Volume 2010 (2010), Article ID 412160, 16 pages
doi:10.1155/2010/412160
Research Article

Fuzzy Stability of Quadratic Functional Equations

Jung Rye Lee,1 Sun-Young Jang,2 Choonkil Park,3 and Dong Yun Shin4

1Department of Mathematics, Daejin University, Kyeonggi 487-711, Republic of Korea
2Department of Mathematics, University of Ulsan, Ulsan 680-749, Republic of Korea
3Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Republic of Korea
4Department of Mathematics, University of Seoul, Seoul 130-743, Republic of Korea

Received 10 February 2010; Accepted 11 April 2010

Academic Editor: T. Bhaskar

Copyright © 2010 Jung Rye Lee 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

The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations f(x+y)+f(x−y)=2f(x)+2f(y) and f(ax+by)+f(ax−by)=2a2f(x)+2b2f(y)  (a,b∈ℝ\{0},a≠±1) in fuzzy Banach spaces.