Abstract and Applied Analysis
Volume 2012 (2012), Article ID 235359, 14 pages
http://dx.doi.org/10.1155/2012/235359
Research Article

On the Stability of a Parametric Additive Functional Equation in Quasi-Banach Spaces

A. Ebadian,1 N. Ghobadipour,2 and M. Eshaghi Gordji3

1Department of Mathematics, Payame Noor University, P.O. BOX 19395-3697, Tehran, Iran
2Department of Mathematics, Urmia University, Urmia, Iran
3Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran

Received 22 January 2012; Revised 16 February 2012; Accepted 16 February 2012

Academic Editor: Narcisa C. Apreutesei

Copyright © 2012 A. Ebadian 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 investigate the generalized Hyers-Ulam stability of the following functional equation ∑ 𝑚 𝑖 = 1 𝑓 ( 𝑥 𝑖 ) = 1 / 2 𝑚 [ ∑ 𝑚 𝑖 = 1 𝑓 ( 𝑚 𝑥 𝑖 + ∑ 𝑚 𝑗 = 1 , 𝑗 ≠ 𝑖 𝑥 𝑗 ) + 𝑓 ( ∑ 𝑚 𝑖 = 1 𝑥 𝑖 ) ] for a fixed positive integer 𝑚 with 𝑚 ≥ 2 in quasi-Banach spaces.