Abstract and Applied Analysis
Volume 2008 (2008), Article ID 135237, 10 pages
Research Article

A Functional Equation Originating from Elliptic Curves

Won-Gil Park1 and Jae-Hyeong Bae2

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

Received 17 November 2007; Revised 1 February 2008; Accepted 5 April 2008

Academic Editor: John Rassias

Copyright © 2008 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.


We obtain the general solution and the stability of the functional equation f(x+y+z,u+v+w)+f(x+yz,u+v+w)+2f(x,uw)+2f(y,vw)=f(x+y,u+w)+f(x+y,v+w)+f(x+z,u+w)+f(xz,u+vw)+f(y+z,v+w)+f(yz,u+vw). The function f(x,y)=x3+ax+by2 having level curves as elliptic curves is a solution of the above functional equation.