Abstract and Applied Analysis
Volume 2011 (2011), Article ID 326951, 19 pages
http://dx.doi.org/10.1155/2011/326951
Research Article

Solutions and the Generalized Hyers-Ulam-Rassias Stability of a Generalized Quadratic-Additive Functional Equation

M. Janfada and R. Shourvazi

Department of Mathematics, Sabzevar Tarbiat Moallem University, P.O. Box 397, Sabzevar, Iran

Received 23 January 2011; Revised 5 April 2011; Accepted 26 April 2011

Academic Editor: D. Anderson

Copyright © 2011 M. Janfada and R. Shourvazi. 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 study general solutions and generalized Hyers-Ulam-Rassias stability of the following 𝑛 -dimensional functional equation ∑ 𝑓 ( 𝑘 𝑖 = 1 𝑥 𝑖 ∑ ) + ( 𝑘 − 2 ) 𝑘 𝑖 = 1 𝑓 ( 𝑥 𝑖 ∑ ) = 𝑘 𝑖 = 1 ∑ 𝑘 𝑗 = 1 , 𝑗 > 𝑖 𝑓 ( 𝑥 𝑖 + 𝑥 𝑗 ) , 𝑘 ≥ 3 , on non-Archimedean normed spaces.