International Journal of Mathematics and Mathematical Sciences 
Volume 2003 (2003), Issue 1, Pages 15-26
doi:10.1155/S016117120311037X

Local stability of the additive functional equation and its applications

Soon-Mo Jung and Byungbae Kim

 Mathematics Section, College of Science and Technology, Hong-Ik University, Chochiwon 339-701, Korea
Received 5 October 2001

Abstract

The main purpose of this paper is to prove the Hyers-Ulam stability of the additive functional equation for a large class of unbounded domains. Furthermore, by using the theorem, we prove the stability of Jensen's functional equation for a large class of restricted domains.