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Journal of Function Spaces
Volume 2014, Article ID 153610, 7 pages
http://dx.doi.org/10.1155/2014/153610
Research Article

Stability of Pexider Equations on Semigroup with No Neutral Element

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

Received 2 February 2014; Revised 18 March 2014; Accepted 22 March 2014; Published 10 April 2014

Academic Editor: Krzysztof Ciepliński

Copyright © 2014 Jaeyoung 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

Let be a commutative semigroup with no neutral element, a Banach space, and the set of complex numbers. In this paper we prove the Hyers-Ulam stability for Pexider equation for all , where . Using Jung’s theorem we obtain a better bound than that usually obtained. Also, generalizing the result of Baker (1980) we prove the superstability for Pexider-exponential equation for all , where . As a direct consequence of the result we also obtain the general solutions of the Pexider-exponential equation for all , a closed form of which is not yet known.