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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 435310, 15 pages
http://dx.doi.org/10.1155/2012/435310
Research Article

On a Stability of Logarithmic-Type Functional Equation in Schwartz Distributions

Department of Mathematics, Kunsan National University, Kunsan 573-701, Republic of Korea

Received 29 August 2012; Accepted 18 October 2012

Academic Editor: Abdelghani Bellouquid

Copyright © 2012 Jae-Young Chung. 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 prove the Hyers-Ulam stability of the logarithmic functional equation of Heuvers and Kannappan , in both classical and distributional senses. As a classical sense, the Hyers-Ulam stability of the inequality will be proved, where . As a distributional analogue of the above inequality, the stability of inequality will be proved, where and denotes the pullback of distributions.