Properties of convergence of a class of iterative processes generated by sequences of self-mappings with applications to switched dynamic systems

This article investigates the convergence properties of iterative processes involving sequences of self-mappings of metric or Banach spaces. Such sequences are built from a set of primary self-mappings which are either expansive or non-expansive self-mappings and some of the non-expansive ones can b...

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Detalles Bibliográficos
Autores: De la Sen Parte, Manuel, Ibeas Hernández, Asier
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universidad del País Vasco
Repositorio:Addi. Archivo Digital para la Docencia y la Investigación
OAI Identifier:oai:addi.ehu.eus:10810/15738
Acceso en línea:http://hdl.handle.net/10810/15738
Access Level:acceso abierto
Palabra clave:discrete-continuous systems
time-invariant systems
proximity points
differential-equations
adaptive-control
cyclic mappings
metric-spaces
stability
delays
positivity
expansive
non-expansive
contractive and strictly contractive self-mappings
switched dynamic systems
convergence
fixed point
ANALYSIS
DISCRETE MATHEMATICS AND COMBINATORICS
MATHEMATICS, APPLIED
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spelling Properties of convergence of a class of iterative processes generated by sequences of self-mappings with applications to switched dynamic systemsDe la Sen Parte, ManuelIbeas Hernández, Asierdiscrete-continuous systemstime-invariant systemsproximity pointsdifferential-equationsadaptive-controlcyclic mappingsmetric-spacesstabilitydelayspositivityexpansivenon-expansivecontractive and strictly contractive self-mappingsswitched dynamic systemsconvergencefixed pointANALYSISDISCRETE MATHEMATICS AND COMBINATORICSMATHEMATICS, APPLIEDThis article investigates the convergence properties of iterative processes involving sequences of self-mappings of metric or Banach spaces. Such sequences are built from a set of primary self-mappings which are either expansive or non-expansive self-mappings and some of the non-expansive ones can be contractive including the case of strict contractions. The sequences are built subject to switching laws which select each active self-mapping on a certain activation interval in such a way that essential properties of boundedness and convergence of distances and iterated sequences are guaranteed. Applications to the important problem of stability of dynamic switched systems are also given.The authors are very grateful to the Spanish Government for Grant DPI2012-30651 and to the Basque Government and UPV/EHU for Grants IT378-10, SAIOTEK S-PE13UN039 and UFI 2011/07. The authors are also grateful to the referees for their suggestions.Springer International Publishing201520152014info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10810/15738reponame:Addi. Archivo Digital para la Docencia y la Investigacióninstname:Universidad del País VascoIngléshttp://www.journalofinequalitiesandapplications.com/content/2014/1/498/abstractinfo:eu-repo/semantics/openAccess2014 Sen and Ibeas; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.oai:addi.ehu.eus:10810/157382026-06-18T09:23:17Z
dc.title.none.fl_str_mv Properties of convergence of a class of iterative processes generated by sequences of self-mappings with applications to switched dynamic systems
title Properties of convergence of a class of iterative processes generated by sequences of self-mappings with applications to switched dynamic systems
spellingShingle Properties of convergence of a class of iterative processes generated by sequences of self-mappings with applications to switched dynamic systems
De la Sen Parte, Manuel
discrete-continuous systems
time-invariant systems
proximity points
differential-equations
adaptive-control
cyclic mappings
metric-spaces
stability
delays
positivity
expansive
non-expansive
contractive and strictly contractive self-mappings
switched dynamic systems
convergence
fixed point
ANALYSIS
DISCRETE MATHEMATICS AND COMBINATORICS
MATHEMATICS, APPLIED
title_short Properties of convergence of a class of iterative processes generated by sequences of self-mappings with applications to switched dynamic systems
title_full Properties of convergence of a class of iterative processes generated by sequences of self-mappings with applications to switched dynamic systems
title_fullStr Properties of convergence of a class of iterative processes generated by sequences of self-mappings with applications to switched dynamic systems
title_full_unstemmed Properties of convergence of a class of iterative processes generated by sequences of self-mappings with applications to switched dynamic systems
title_sort Properties of convergence of a class of iterative processes generated by sequences of self-mappings with applications to switched dynamic systems
dc.creator.none.fl_str_mv De la Sen Parte, Manuel
Ibeas Hernández, Asier
author De la Sen Parte, Manuel
author_facet De la Sen Parte, Manuel
Ibeas Hernández, Asier
author_role author
author2 Ibeas Hernández, Asier
author2_role author
dc.subject.none.fl_str_mv discrete-continuous systems
time-invariant systems
proximity points
differential-equations
adaptive-control
cyclic mappings
metric-spaces
stability
delays
positivity
expansive
non-expansive
contractive and strictly contractive self-mappings
switched dynamic systems
convergence
fixed point
ANALYSIS
DISCRETE MATHEMATICS AND COMBINATORICS
MATHEMATICS, APPLIED
topic discrete-continuous systems
time-invariant systems
proximity points
differential-equations
adaptive-control
cyclic mappings
metric-spaces
stability
delays
positivity
expansive
non-expansive
contractive and strictly contractive self-mappings
switched dynamic systems
convergence
fixed point
ANALYSIS
DISCRETE MATHEMATICS AND COMBINATORICS
MATHEMATICS, APPLIED
description This article investigates the convergence properties of iterative processes involving sequences of self-mappings of metric or Banach spaces. Such sequences are built from a set of primary self-mappings which are either expansive or non-expansive self-mappings and some of the non-expansive ones can be contractive including the case of strict contractions. The sequences are built subject to switching laws which select each active self-mapping on a certain activation interval in such a way that essential properties of boundedness and convergence of distances and iterated sequences are guaranteed. Applications to the important problem of stability of dynamic switched systems are also given.
publishDate 2014
dc.date.none.fl_str_mv 2014
2015
2015
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10810/15738
url http://hdl.handle.net/10810/15738
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv http://www.journalofinequalitiesandapplications.com/content/2014/1/498/abstract
dc.rights.none.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 Springer International Publishing
publisher.none.fl_str_mv Springer International Publishing
dc.source.none.fl_str_mv reponame:Addi. Archivo Digital para la Docencia y la Investigación
instname:Universidad del País Vasco
instname_str Universidad del País Vasco
reponame_str Addi. Archivo Digital para la Docencia y la Investigación
collection Addi. Archivo Digital para la Docencia y la Investigación
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301629

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