Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 912046, 8 pages
doi:10.1155/2009/912046
Research Article

A Fixed Point Approach to the Stability of the Functional Equation f(x+y)=F[f(x),f(y)]

Soon-Mo Jung1 and Seungwook Min2

1Mathematics Section, College of Science and Technology, Hongik University, Jochiwon 339-701, South Korea
2Division of Computer Science, Sangmyung University, 7 Hongji-dong, Jongno-gu, Seoul 110-743, South Korea

Received 20 July 2009; Revised 20 September 2009; Accepted 30 September 2009

Academic Editor: Massimo Furi

Copyright © 2009 Soon-Mo Jung and Seungwook Min. 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

By applying the fixed point method, we will prove the Hyers-Ulam-Rassias stability of the functional equation f(x+y)=F[f(x),f(y)] under some additional assumptions on the function F and spaces involved.