On Ulam's Type Stability of the Cauchy Additive Equation

We prove a general result on Ulam's type stability of the functional equation f(x + y) = f(x) + f(y), 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 t...

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Detalles Bibliográficos
Autor principal: Brzdęk, Janusz
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3970066/
https://www.ncbi.nlm.nih.gov/pubmed/24715815
http://dx.doi.org/10.1155/2014/540164
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author Brzdęk, Janusz
author_facet Brzdęk, Janusz
author_sort Brzdęk, Janusz
collection PubMed
description We prove a general result on Ulam's type stability of the functional equation f(x + y) = f(x) + f(y), 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.
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spelling pubmed-39700662014-04-08 On Ulam's Type Stability of the Cauchy Additive Equation Brzdęk, Janusz ScientificWorldJournal Research Article We prove a general result on Ulam's type stability of the functional equation f(x + y) = f(x) + f(y), 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. Hindawi Publishing Corporation 2014-03-16 /pmc/articles/PMC3970066/ /pubmed/24715815 http://dx.doi.org/10.1155/2014/540164 Text en Copyright © 2014 Janusz Brzdęk. https://creativecommons.org/licenses/by/3.0/ 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.
spellingShingle Research Article
Brzdęk, Janusz
On Ulam's Type Stability of the Cauchy Additive Equation
title On Ulam's Type Stability of the Cauchy Additive Equation
title_full On Ulam's Type Stability of the Cauchy Additive Equation
title_fullStr On Ulam's Type Stability of the Cauchy Additive Equation
title_full_unstemmed On Ulam's Type Stability of the Cauchy Additive Equation
title_short On Ulam's Type Stability of the Cauchy Additive Equation
title_sort on ulam's type stability of the cauchy additive equation
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3970066/
https://www.ncbi.nlm.nih.gov/pubmed/24715815
http://dx.doi.org/10.1155/2014/540164
work_keys_str_mv AT brzdekjanusz onulamstypestabilityofthecauchyadditiveequation

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