Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 140767, 15 pages
Research Article

The Fixed Point Method for Fuzzy Approximation of a Functional Equation Associated with Inner Product Spaces

Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran

Received 3 July 2010; Accepted 11 September 2010

Academic Editor: John Rassias

Copyright © 2010 M. Eshaghi Gordji and H. Khodaei. 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.


Th. M. Rassias (1984) proved that the norm defined over a real vector space X is induced by an inner product if and only if for a fixed integer n2,  i=1nxi-(1/n)j=1nxj2=i=1nxi2-n(1/n)i=1nxi2 holds for all x1,,xnX. The aim of this paper is to extend the applications of the fixed point alternative method to provide a fuzzy stability for the functional equation i=1nf(xi-(1/n)j=1nxj)=i=1nf(xi)-nf((1/n)i=1nxi) which is said to be a functional equation associated with inner product spaces.