On Some Properties of a Class of Eventually Locally Mixed Cyclic/Acyclic Multivalued Self-Mappings with Application Examples

In this paper, a multivalued self-mapping is defined on the union of a finite number of subsets (Formula presented.) of a metric space which is, in general, of a mixed cyclic and acyclic nature in the sense that it can perform some iterations within each of the subsets before executing a switching a...

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Autores: De la Sen, Manuel|||0000-0001-9320-9433, Ibeas, Asier|||0000-0001-5094-3152
Formato: artículo
Fecha de publicación:2022
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:272337
Acesso em linha:https://ddd.uab.cat/record/272337
https://dx.doi.org/urn:doi:10.3390/math10142415
Access Level:acceso abierto
Palavra-chave:Cyclic self-mappings
Cyclic contractions
Mixed cyclic/acyclic self-mappings
Uniformly convex Banach space
Impulsive dynamic systems
Stabilization
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spelling On Some Properties of a Class of Eventually Locally Mixed Cyclic/Acyclic Multivalued Self-Mappings with Application ExamplesDe la Sen, Manuel|||0000-0001-9320-9433Ibeas, Asier|||0000-0001-5094-3152Cyclic self-mappingsCyclic contractionsMixed cyclic/acyclic self-mappingsUniformly convex Banach spaceImpulsive dynamic systemsStabilizationIn this paper, a multivalued self-mapping is defined on the union of a finite number of subsets (Formula presented.) of a metric space which is, in general, of a mixed cyclic and acyclic nature in the sense that it can perform some iterations within each of the subsets before executing a switching action to its right adjacent one when generating orbits. The self-mapping can have combinations of locally contractive, non-contractive/non-expansive and locally expansive properties for some of the switching between different pairs of adjacent subsets. The properties of the asymptotic boundedness of the distances associated with the elements of the orbits are achieved under certain conditions of the global dominance of the contractivity of groups of consecutive iterations of the self-mapping, with each of those groups being of non-necessarily fixed size. If the metric space is a uniformly convex Banach one and the subsets are closed and convex, then some particular results on the convergence of the sequences of iterates to the best proximity points of the adjacent subsets are obtained in the absence of eventual local expansivity for switches between all the pairs of adjacent subsets. An application of the stabilization of a discrete dynamic system subject to impulsive effects in its dynamics due to finite discontinuity jumps in its state is also discussed. 22022-01-0120222022-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/272337https://dx.doi.org/urn:doi:10.3390/math10142415reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgencia Estatal de Investigación https://doi.org/10.13039/501100011033 RTI2018-094336-B-I00open accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2723372026-06-06T12:50:31Z
dc.title.none.fl_str_mv On Some Properties of a Class of Eventually Locally Mixed Cyclic/Acyclic Multivalued Self-Mappings with Application Examples
title On Some Properties of a Class of Eventually Locally Mixed Cyclic/Acyclic Multivalued Self-Mappings with Application Examples
spellingShingle On Some Properties of a Class of Eventually Locally Mixed Cyclic/Acyclic Multivalued Self-Mappings with Application Examples
De la Sen, Manuel|||0000-0001-9320-9433
Cyclic self-mappings
Cyclic contractions
Mixed cyclic/acyclic self-mappings
Uniformly convex Banach space
Impulsive dynamic systems
Stabilization
title_short On Some Properties of a Class of Eventually Locally Mixed Cyclic/Acyclic Multivalued Self-Mappings with Application Examples
title_full On Some Properties of a Class of Eventually Locally Mixed Cyclic/Acyclic Multivalued Self-Mappings with Application Examples
title_fullStr On Some Properties of a Class of Eventually Locally Mixed Cyclic/Acyclic Multivalued Self-Mappings with Application Examples
title_full_unstemmed On Some Properties of a Class of Eventually Locally Mixed Cyclic/Acyclic Multivalued Self-Mappings with Application Examples
title_sort On Some Properties of a Class of Eventually Locally Mixed Cyclic/Acyclic Multivalued Self-Mappings with Application Examples
dc.creator.none.fl_str_mv De la Sen, Manuel|||0000-0001-9320-9433
Ibeas, Asier|||0000-0001-5094-3152
author De la Sen, Manuel|||0000-0001-9320-9433
author_facet De la Sen, Manuel|||0000-0001-9320-9433
Ibeas, Asier|||0000-0001-5094-3152
author_role author
author2 Ibeas, Asier|||0000-0001-5094-3152
author2_role author
dc.subject.none.fl_str_mv Cyclic self-mappings
Cyclic contractions
Mixed cyclic/acyclic self-mappings
Uniformly convex Banach space
Impulsive dynamic systems
Stabilization
topic Cyclic self-mappings
Cyclic contractions
Mixed cyclic/acyclic self-mappings
Uniformly convex Banach space
Impulsive dynamic systems
Stabilization
description In this paper, a multivalued self-mapping is defined on the union of a finite number of subsets (Formula presented.) of a metric space which is, in general, of a mixed cyclic and acyclic nature in the sense that it can perform some iterations within each of the subsets before executing a switching action to its right adjacent one when generating orbits. The self-mapping can have combinations of locally contractive, non-contractive/non-expansive and locally expansive properties for some of the switching between different pairs of adjacent subsets. The properties of the asymptotic boundedness of the distances associated with the elements of the orbits are achieved under certain conditions of the global dominance of the contractivity of groups of consecutive iterations of the self-mapping, with each of those groups being of non-necessarily fixed size. If the metric space is a uniformly convex Banach one and the subsets are closed and convex, then some particular results on the convergence of the sequences of iterates to the best proximity points of the adjacent subsets are obtained in the absence of eventual local expansivity for switches between all the pairs of adjacent subsets. An application of the stabilization of a discrete dynamic system subject to impulsive effects in its dynamics due to finite discontinuity jumps in its state is also discussed.
publishDate 2022
dc.date.none.fl_str_mv 2
2022-01-01
2022
2022-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/272337
https://dx.doi.org/urn:doi:10.3390/math10142415
url https://ddd.uab.cat/record/272337
https://dx.doi.org/urn:doi:10.3390/math10142415
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 RTI2018-094336-B-I00
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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