Stability of the Exponential Functional Equation in Riesz Algebras

Stability of the Exponential Functional Equation in Riesz Algebras

We deal with the stability of the exponential Cauchy functional equation F(x+y)=F(x)F(y) in the class of functions F:G→L mapping a group (G, +) into a Riesz algebra L. 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 n...

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Main Author: Bogdan Batko
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/848540
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spelling doaj-00c5816e88ec4ec183ee17a5ba73c5852020-11-24T22:18:44ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/848540848540Stability of the Exponential Functional Equation in Riesz AlgebrasBogdan Batko0Institute of Mathematics, Pedagogical University of Cracow, Podchorążych 2, 30-084 Kraków, PolandWe deal with the stability of the exponential Cauchy functional equation F(x+y)=F(x)F(y) in the class of functions F:G→L mapping a group (G, +) into a Riesz algebra L. 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.http://dx.doi.org/10.1155/2014/848540
collection DOAJ
language English
format Article
sources DOAJ
author Bogdan Batko
spellingShingle Bogdan Batko
Stability of the Exponential Functional Equation in Riesz Algebras
Abstract and Applied Analysis
author_facet Bogdan Batko
author_sort Bogdan Batko
title Stability of the Exponential Functional Equation in Riesz Algebras
title_short Stability of the Exponential Functional Equation in Riesz Algebras
title_full Stability of the Exponential Functional Equation in Riesz Algebras
title_fullStr Stability of the Exponential Functional Equation in Riesz Algebras
title_full_unstemmed Stability of the Exponential Functional Equation in Riesz Algebras
title_sort stability of the exponential functional equation in riesz algebras
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description We deal with the stability of the exponential Cauchy functional equation F(x+y)=F(x)F(y) in the class of functions F:G→L mapping a group (G, +) into a Riesz algebra L. 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.
url http://dx.doi.org/10.1155/2014/848540
work_keys_str_mv AT bogdanbatko stabilityoftheexponentialfunctionalequationinrieszalgebras
_version_ 1725781932447367168

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