Abstract and Applied Analysis
Volume 2012 (2012), Article ID 953938, 22 pages
http://dx.doi.org/10.1155/2012/953938
Research Article

Solution and Hyers-Ulam-Rassias Stability of Generalized Mixed Type Additive-Quadratic Functional Equations in Fuzzy Banach Spaces

M. Eshaghi Gordji,1 H. Azadi Kenary,2 H. Rezaei,2 Y. W. Lee,3 and G. H. Kim4

1Department of Mathematics, Semnan University, Semnan 35131-19111, Iran
2Department of Mathematics, Yasouj University, Yasouj 75918-74831, Iran
3Department of Computer Hacking and Information Security, Daejeon University, Youngwoondong Donggu, Daejeon 300-716, Republic of Korea
4Department of Mathematics, Kangnam University, Yongin, Gyeonggi 446-702, Republic of Korea

Received 19 November 2011; Revised 21 January 2012; Accepted 13 February 2012

Academic Editor: Gerd Teschke

Copyright © 2012 M. Eshaghi Gordji 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

By using fixed point methods and direct method, we establish the generalized Hyers-Ulam stability of the following additive-quadratic functional equation 𝑓 ( 𝑥 + 𝑘 𝑦 ) + 𝑓 ( 𝑥 − 𝑘 𝑦 ) = 𝑓 ( 𝑥 + 𝑦 ) + 𝑓 ( 𝑥 − 𝑦 ) + ( 2 ( 𝑘 + 1 ) / 𝑘 ) 𝑓 ( 𝑘 𝑦 ) − 2 ( 𝑘 + 1 ) 𝑓 ( 𝑦 ) for fixed integers 𝑘 with 𝑘 ≠ 0 , ± 1 in fuzzy Banach spaces.