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

Recommended by Vijay Gupta

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.