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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 848540, 4 pages
http://dx.doi.org/10.1155/2014/848540
Research Article

Stability of the Exponential Functional Equation in Riesz Algebras

1Institute of Mathematics, Pedagogical University of Cracow, Podchorążych 2, 30-084 Kraków, Poland
2Department of Computational Mathematics, WSB–NLU, Zielona 27, 33-300 Nowy Sącz, Poland

Received 5 July 2013; Accepted 19 December 2013; Published 5 January 2014

Academic Editor: Józef Banaś

Copyright © 2014 Bogdan Batko. 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 deal with the stability of the exponential Cauchy functional equation in the class of functions mapping a group (, +) into a Riesz algebra . The main aim of this paper is to prove that the exponential Cauchy functional equation is stable in the sense of Hyers-Ulam and is not superstable in the sense of Baker. To prove the stability we use the Yosida Spectral Representation Theorem.