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