Abstract and Applied Analysis
Volume 2008 (2008), Article ID 136592, 11 pages
Functional Inequalities Associated with Additive Mappings
1Department of Mathematics, Hallym University, Chuncheon 200-702, South Korea
2Department of Mathematics, Mokwon University, Daejeon 302-729, South Korea
Received 13 May 2008; Revised 25 June 2008; Accepted 1 August 2008
Academic Editor: John Rassias
Copyright © 2008 Jaiok Roh and Ick-Soon Chang. 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.
The functional inequality is investigated, where is a group divisible by and are mappings, and is a Banach space. The main result of the paper states that the assumptions above together with (1) and (2) , or , imply that is additive. In addition, some stability theorems are proved.