Approximation of the generalized Cauchy–Jensen functional equation in [Formula: see text] -algebras

In this paper, we prove Hyers–Ulam–Rassias stability of [Formula: see text] -algebra homomorphisms for the following generalized Cauchy–Jensen equation: [Formula: see text] for all [Formula: see text] and for any fixed positive integer [Formula: see text] , which was introduced by Gao et al. [J. Mat...

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Autores principales: Kaskasem, Prondanai, Klin-eam, Chakkrid
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6154084/
https://www.ncbi.nlm.nih.gov/pubmed/30839670
http://dx.doi.org/10.1186/s13660-018-1824-6
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author Kaskasem, Prondanai
Klin-eam, Chakkrid
author_facet Kaskasem, Prondanai
Klin-eam, Chakkrid
author_sort Kaskasem, Prondanai
collection PubMed
description In this paper, we prove Hyers–Ulam–Rassias stability of [Formula: see text] -algebra homomorphisms for the following generalized Cauchy–Jensen equation: [Formula: see text] for all [Formula: see text] and for any fixed positive integer [Formula: see text] , which was introduced by Gao et al. [J. Math. Inequal. 3:63–77, 2009], on [Formula: see text] -algebras by using fixed poind alternative theorem. Moreover, we introduce and investigate Hyers–Ulam–Rassias stability of generalized θ-derivation for such functional equations on [Formula: see text] -algebras by the same method.
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spelling pubmed-61540842018-10-10 Approximation of the generalized Cauchy–Jensen functional equation in [Formula: see text] -algebras Kaskasem, Prondanai Klin-eam, Chakkrid J Inequal Appl Research In this paper, we prove Hyers–Ulam–Rassias stability of [Formula: see text] -algebra homomorphisms for the following generalized Cauchy–Jensen equation: [Formula: see text] for all [Formula: see text] and for any fixed positive integer [Formula: see text] , which was introduced by Gao et al. [J. Math. Inequal. 3:63–77, 2009], on [Formula: see text] -algebras by using fixed poind alternative theorem. Moreover, we introduce and investigate Hyers–Ulam–Rassias stability of generalized θ-derivation for such functional equations on [Formula: see text] -algebras by the same method. Springer International Publishing 2018-09-12 2018 /pmc/articles/PMC6154084/ /pubmed/30839670 http://dx.doi.org/10.1186/s13660-018-1824-6 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Kaskasem, Prondanai
Klin-eam, Chakkrid
Approximation of the generalized Cauchy–Jensen functional equation in [Formula: see text] -algebras
title Approximation of the generalized Cauchy–Jensen functional equation in [Formula: see text] -algebras
title_full Approximation of the generalized Cauchy–Jensen functional equation in [Formula: see text] -algebras
title_fullStr Approximation of the generalized Cauchy–Jensen functional equation in [Formula: see text] -algebras
title_full_unstemmed Approximation of the generalized Cauchy–Jensen functional equation in [Formula: see text] -algebras
title_short Approximation of the generalized Cauchy–Jensen functional equation in [Formula: see text] -algebras
title_sort approximation of the generalized cauchy–jensen functional equation in [formula: see text] -algebras
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6154084/
https://www.ncbi.nlm.nih.gov/pubmed/30839670
http://dx.doi.org/10.1186/s13660-018-1824-6
work_keys_str_mv AT kaskasemprondanai approximationofthegeneralizedcauchyjensenfunctionalequationinformulaseetextalgebras
AT klineamchakkrid approximationofthegeneralizedcauchyjensenfunctionalequationinformulaseetextalgebras

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