Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 24716, 8 pages
doi:10.1155/2007/24716
Research Article

A Multidimensional Functional Equation Having Quadratic Forms as Solutions

Won-Gil Park1 and Jae-Hyeong Bae2

1National Institute for Mathematical Sciences, 385-16 Doryong-Dong, Yuseong-Gu, Daejeon 305-340, South Korea
2Department of Applied Mathematics, Kyung Hee University, Yongin 449-701, South Korea

Received 7 July 2007; Accepted 3 September 2007

Academic Editor: Vijay Gupta

Copyright © 2007 Won-Gil Park and Jae-Hyeong Bae. 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 obtain the general solution and the stability of the m-variable quadratic functional equation f(x1+y1,…,xm+ym)+f(x1−y1,…,xm−ym)=2f(x1,…,xm)+2f(y1,…,ym). The quadratic form f(x1,…,xm)=∑1≤i≤j≤maijxixj is a solution of the given functional equation.