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The Scientific World Journal
Volume 2014, Article ID 540164, 7 pages
http://dx.doi.org/10.1155/2014/540164
Research Article

On Ulam's Type Stability of the Cauchy Additive Equation

Department of Mathematics, Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland

Received 27 August 2013; Accepted 8 December 2013; Published 16 March 2014

Academic Editors: N. Kallur and P. Yang

Copyright © 2014 Janusz Brzdęk. 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 a general result on Ulam's type stability of the functional equation , in the class of functions mapping a commutative group into a commutative group. As a consequence, we deduce from it some hyperstability outcomes. Moreover, we also show how to use that result to improve some earlier stability estimations given by Isaac and Rassias.