Convergence Criteria for Fixed Point Problems and Differential Equations

Autores
Sofonea, Mircea; Tarzia, Domingo Alberto
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider a Cauchy problem for differential equations in a Hilbert space X. The problem is stated in a time interval I, which can be finite or infinite. We use a fixed point argument for history-dependent operators to prove the unique solvability of the problem. Then, we establish convergence criteria for both a general fixed point problem and the corresponding Cauchy problem. These criteria provide the necessary and sufficient conditions on a sequence (Formula presented.), which guarantee its convergence to the solution of the corresponding problem, in the space of both continuous and continuously differentiable functions. We then specify our results in the study of a particular differential equation governed by two nonlinear operators. Finally, we provide an application in viscoelasticity and give a mechanical interpretation of the corresponding convergence result.
Fil: Sofonea, Mircea. Université de Perpignan Via Domitia; Francia
Fil: Tarzia, Domingo Alberto. Universidad Austral; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
CAUCHY PROBLEM
CONVERGENCE CRITERION
DIFFERENTIAL EQUATION
FIXED POINT
HISTORY-DEPENDENT OPERATOR
VISCOELASTIC CONSTITUTIVE LAW
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/230908
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/230908
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Convergence Criteria for Fixed Point Problems and Differential EquationsSofonea, MirceaTarzia, Domingo AlbertoCAUCHY PROBLEMCONVERGENCE CRITERIONDIFFERENTIAL EQUATIONFIXED POINTHISTORY-DEPENDENT OPERATORVISCOELASTIC CONSTITUTIVE LAWhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider a Cauchy problem for differential equations in a Hilbert space X. The problem is stated in a time interval I, which can be finite or infinite. We use a fixed point argument for history-dependent operators to prove the unique solvability of the problem. Then, we establish convergence criteria for both a general fixed point problem and the corresponding Cauchy problem. These criteria provide the necessary and sufficient conditions on a sequence (Formula presented.), which guarantee its convergence to the solution of the corresponding problem, in the space of both continuous and continuously differentiable functions. We then specify our results in the study of a particular differential equation governed by two nonlinear operators. Finally, we provide an application in viscoelasticity and give a mechanical interpretation of the corresponding convergence result.Fil: Sofonea, Mircea. Université de Perpignan Via Domitia; FranciaFil: Tarzia, Domingo Alberto. Universidad Austral; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaMDPI2024-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/230908Sofonea, Mircea; Tarzia, Domingo Alberto; Convergence Criteria for Fixed Point Problems and Differential Equations; MDPI; Mathematics; 12; 3; 2-2024; 1-192227-7390CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.3390/math12030395info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:47:03Zoai:ri.conicet.gov.ar:11336/230908instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:47:03.856CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Convergence Criteria for Fixed Point Problems and Differential Equations
title Convergence Criteria for Fixed Point Problems and Differential Equations
spellingShingle Convergence Criteria for Fixed Point Problems and Differential Equations
Sofonea, Mircea
CAUCHY PROBLEM
CONVERGENCE CRITERION
DIFFERENTIAL EQUATION
FIXED POINT
HISTORY-DEPENDENT OPERATOR
VISCOELASTIC CONSTITUTIVE LAW
title_short Convergence Criteria for Fixed Point Problems and Differential Equations
title_full Convergence Criteria for Fixed Point Problems and Differential Equations
title_fullStr Convergence Criteria for Fixed Point Problems and Differential Equations
title_full_unstemmed Convergence Criteria for Fixed Point Problems and Differential Equations
title_sort Convergence Criteria for Fixed Point Problems and Differential Equations
dc.creator.none.fl_str_mv Sofonea, Mircea
Tarzia, Domingo Alberto
author Sofonea, Mircea
author_facet Sofonea, Mircea
Tarzia, Domingo Alberto
author_role author
author2 Tarzia, Domingo Alberto
author2_role author
dc.subject.none.fl_str_mv CAUCHY PROBLEM
CONVERGENCE CRITERION
DIFFERENTIAL EQUATION
FIXED POINT
HISTORY-DEPENDENT OPERATOR
VISCOELASTIC CONSTITUTIVE LAW
topic CAUCHY PROBLEM
CONVERGENCE CRITERION
DIFFERENTIAL EQUATION
FIXED POINT
HISTORY-DEPENDENT OPERATOR
VISCOELASTIC CONSTITUTIVE LAW
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We consider a Cauchy problem for differential equations in a Hilbert space X. The problem is stated in a time interval I, which can be finite or infinite. We use a fixed point argument for history-dependent operators to prove the unique solvability of the problem. Then, we establish convergence criteria for both a general fixed point problem and the corresponding Cauchy problem. These criteria provide the necessary and sufficient conditions on a sequence (Formula presented.), which guarantee its convergence to the solution of the corresponding problem, in the space of both continuous and continuously differentiable functions. We then specify our results in the study of a particular differential equation governed by two nonlinear operators. Finally, we provide an application in viscoelasticity and give a mechanical interpretation of the corresponding convergence result.
Fil: Sofonea, Mircea. Université de Perpignan Via Domitia; Francia
Fil: Tarzia, Domingo Alberto. Universidad Austral; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We consider a Cauchy problem for differential equations in a Hilbert space X. The problem is stated in a time interval I, which can be finite or infinite. We use a fixed point argument for history-dependent operators to prove the unique solvability of the problem. Then, we establish convergence criteria for both a general fixed point problem and the corresponding Cauchy problem. These criteria provide the necessary and sufficient conditions on a sequence (Formula presented.), which guarantee its convergence to the solution of the corresponding problem, in the space of both continuous and continuously differentiable functions. We then specify our results in the study of a particular differential equation governed by two nonlinear operators. Finally, we provide an application in viscoelasticity and give a mechanical interpretation of the corresponding convergence result.
publishDate 2024
dc.date.none.fl_str_mv 2024-02
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/230908
Sofonea, Mircea; Tarzia, Domingo Alberto; Convergence Criteria for Fixed Point Problems and Differential Equations; MDPI; Mathematics; 12; 3; 2-2024; 1-19
2227-7390
CONICET Digital
CONICET
url http://hdl.handle.net/11336/230908
identifier_str_mv Sofonea, Mircea; Tarzia, Domingo Alberto; Convergence Criteria for Fixed Point Problems and Differential Equations; MDPI; Mathematics; 12; 3; 2-2024; 1-19
2227-7390
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.3390/math12030395
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1842268834216542208
score 13.13397

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