Table of Contents
ISRN Mathematical Analysis
Volume 2011, Article ID 503164, 8 pages
http://dx.doi.org/10.5402/2011/503164
Research Article

Fuzzy Stability of Quadratic Functional Equations in General Cases

Department of Mathematics, Damghan University, Damghan, Iran

Received 21 February 2011; Accepted 17 April 2011

Academic Editor: W. Sun

Copyright © 2011 Ehsan Movahednia. 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 aim of this paper is to investigate fuzzy Hyers-Ulam-Rassias stability of the general case of quadratic functional equation 𝑓 ( π‘Ž π‘₯ + 𝑏 𝑦 ) + 𝑓 ( π‘Ž π‘₯ βˆ’ 𝑏 𝑦 ) = ( π‘Ž / 2 ) 𝑓 ( π‘₯ + 𝑦 ) + ( π‘Ž / 2 ) 𝑓 ( π‘₯ βˆ’ 𝑦 ) + ( 2 π‘Ž 2 βˆ’ π‘Ž ) 𝑓 ( π‘₯ ) + ( 2 𝑏 2 βˆ’ π‘Ž ) 𝑓 ( 𝑦 ) , where π‘Ž , 𝑏 β‰₯ 1 and fixed integers with π‘Ž β‰  2 𝑏 2 . These functional equations are equivalent. This has been proven by Ulam, 1964.