Different types of Hyers-Ulam-Rassias stabilities for a class of integro-differential equations
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10773/21063 |
Resumo: | We study different kinds of stabilities for a class of very general nonlinear integro-differential equations involving a function which depends on the solutions of the integro-differential equations and on an integral of Volterra type. In particular, we will introduce the notion of {\it semi-Hyers-Ulam-Rassias stability}, which is a type of stability somehow in-between the Hyers-Ulam and Hyers-Ulam-Rassias stabilities. This is considered in a framework of appropriate metric spaces in which sufficient conditions are obtained in view to guarantee Hyers-Ulam-Rassias, semi-Hyers-Ulam-Rassias and Hyers-Ulam stabilities for such a class of integro-differential equations. We will consider the different situations of having the integrals defined on finite and infinite intervals. Among the used techniques, we have fixed point arguments and generalizations of the Bielecki metric. Examples of the application of the proposed theory are included. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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Different types of Hyers-Ulam-Rassias stabilities for a class of integro-differential equationsHyers-Ulam stabilitySemi-Hyers-Ulam-Rassias stabilityHyers-Ulam-Rassias stabilityBanach fixed point theoremIntegro-differential equationWe study different kinds of stabilities for a class of very general nonlinear integro-differential equations involving a function which depends on the solutions of the integro-differential equations and on an integral of Volterra type. In particular, we will introduce the notion of {\it semi-Hyers-Ulam-Rassias stability}, which is a type of stability somehow in-between the Hyers-Ulam and Hyers-Ulam-Rassias stabilities. This is considered in a framework of appropriate metric spaces in which sufficient conditions are obtained in view to guarantee Hyers-Ulam-Rassias, semi-Hyers-Ulam-Rassias and Hyers-Ulam stabilities for such a class of integro-differential equations. We will consider the different situations of having the integrals defined on finite and infinite intervals. Among the used techniques, we have fixed point arguments and generalizations of the Bielecki metric. Examples of the application of the proposed theory are included.Faculty of Sciences and Mathematics, University of Nis, Serbia2017-12-11T11:52:15Z2017-11-30T00:00:00Z2017-11-30info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/21063eng2406-093310.2298/FIL1717379CCastro, L. P.Simões, A. M.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:36:57Zoai:ria.ua.pt:10773/21063Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:53:53.541845Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Different types of Hyers-Ulam-Rassias stabilities for a class of integro-differential equations |
title |
Different types of Hyers-Ulam-Rassias stabilities for a class of integro-differential equations |
spellingShingle |
Different types of Hyers-Ulam-Rassias stabilities for a class of integro-differential equations Castro, L. P. Hyers-Ulam stability Semi-Hyers-Ulam-Rassias stability Hyers-Ulam-Rassias stability Banach fixed point theorem Integro-differential equation |
title_short |
Different types of Hyers-Ulam-Rassias stabilities for a class of integro-differential equations |
title_full |
Different types of Hyers-Ulam-Rassias stabilities for a class of integro-differential equations |
title_fullStr |
Different types of Hyers-Ulam-Rassias stabilities for a class of integro-differential equations |
title_full_unstemmed |
Different types of Hyers-Ulam-Rassias stabilities for a class of integro-differential equations |
title_sort |
Different types of Hyers-Ulam-Rassias stabilities for a class of integro-differential equations |
author |
Castro, L. P. |
author_facet |
Castro, L. P. Simões, A. M. |
author_role |
author |
author2 |
Simões, A. M. |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Castro, L. P. Simões, A. M. |
dc.subject.por.fl_str_mv |
Hyers-Ulam stability Semi-Hyers-Ulam-Rassias stability Hyers-Ulam-Rassias stability Banach fixed point theorem Integro-differential equation |
topic |
Hyers-Ulam stability Semi-Hyers-Ulam-Rassias stability Hyers-Ulam-Rassias stability Banach fixed point theorem Integro-differential equation |
description |
We study different kinds of stabilities for a class of very general nonlinear integro-differential equations involving a function which depends on the solutions of the integro-differential equations and on an integral of Volterra type. In particular, we will introduce the notion of {\it semi-Hyers-Ulam-Rassias stability}, which is a type of stability somehow in-between the Hyers-Ulam and Hyers-Ulam-Rassias stabilities. This is considered in a framework of appropriate metric spaces in which sufficient conditions are obtained in view to guarantee Hyers-Ulam-Rassias, semi-Hyers-Ulam-Rassias and Hyers-Ulam stabilities for such a class of integro-differential equations. We will consider the different situations of having the integrals defined on finite and infinite intervals. Among the used techniques, we have fixed point arguments and generalizations of the Bielecki metric. Examples of the application of the proposed theory are included. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-12-11T11:52:15Z 2017-11-30T00:00:00Z 2017-11-30 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10773/21063 |
url |
http://hdl.handle.net/10773/21063 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
2406-0933 10.2298/FIL1717379C |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Faculty of Sciences and Mathematics, University of Nis, Serbia |
publisher.none.fl_str_mv |
Faculty of Sciences and Mathematics, University of Nis, Serbia |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799137590557802496 |