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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 751680, 9 pages
http://dx.doi.org/10.1155/2013/751680
Research Article

Stability of a Logarithmic Functional Equation in Distributions on a Restricted Domain

1Department of Mathematics, Kunsan National University, Kunsan 573-701, Republic of Korea
2Department of Mathematics, University of Louisville, Louisville, KY 40292, USA

Received 25 May 2013; Accepted 2 August 2013

Academic Editor: Soon-Mo Jung

Copyright © 2013 Jaeyoung Chung and Prasanna K. Sahoo. 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

Let be the set of real numbers, , , and . As classical and versions of the Hyers-Ulam stability of the logarithmic type functional equation in a restricted domain, we consider the following inequalities: , and in the sectors . As consequences of the results, we obtain asymptotic behaviors of the previous inequalities. We also consider its distributional version , where , , , , , and the inequality means that for all test functions .