Abstract and Applied Analysis
Volume 2007 (2007), Article ID 45179, 10 pages
doi:10.1155/2007/45179
Research Article

On a Cubic Equation and a Jensen-Quadratic Equation

Jae-Hyeong Bae1 and Won-Gil Park2

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

Received 29 September 2007; Accepted 20 November 2007

Academic Editor: Elena Litsyn

Copyright © 2007 Jae-Hyeong Bae and Won-Gil Park. 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 solutions of the cubic functional equation 3[g(x+y)+g(x−y)+6g(x)]=2g(2x+y)+2g(2x−y)+g(−x−y)+g(−x+y)+6g(−x) and the Jensen-quadratic functional equation f((x+y)/2,z+w)+f((x+y)/2,z−w)=f(x,z)+f(x,w)+f(y,z)+f(y,w).