Journal of Applied Mathematics
Volume 2012 (2012), Article ID 691981, 12 pages
http://dx.doi.org/10.1155/2012/691981
Research Article

Stability of Jensen-Type Functional Equations on Restricted Domains in a Group and Their Asymptotic Behaviors

Jae-Young Chung,1 Dohan Kim,2 and John Michael Rassias3

1Department of Mathematics, Kunsan National University, Kunsan 573-701, Republic of Korea
2Department of Mathematics, Seoul National University, Seoul 151-747, Republic of Korea
3Section of Mathematics and Informatics, Pedagogical Department E. E., National and Kapodistrian University of Athens, 4 Agamemnonos Street, Aghia Paraskevi, 15342 Athens, Greece

Received 20 June 2011; Accepted 5 September 2011

Academic Editor: Junjie Wei

Copyright © 2012 Jae-Young Chung et al. 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

We consider the Hyers-Ulam stability problems for the Jensen-type functional equations in general restricted domains. The main purpose of this paper is to find the restricted domains for which the functional inequality satisfied in those domains extends to the inequality for whole domain. As consequences of the results we obtain asymptotic behavior of the equations.