Recurrence relations for a family of iterations assuming Holder continuous second order Frechet derivative

[EN] The semilocal convergence using recurrence relations of a family of iterations for solving nonlinear equations in Banach spaces is established. It is done under the assumption that the second order Frechet derivative satisfies the Holder continuity condition. This condition is more general than...

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Autores: Gupta, Dharmendra Kumar, Singh, Sukhjit, Hueso, Jose Luis, Srivastava, Shwetabh, Kumar, Abhimanyu, Martínez Molada, Eulalia|||0000-0003-2869-4334
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/182191
Acceso en línea:https://riunet.upv.es/handle/10251/182191
Access Level:acceso abierto
Palabra clave:Dynamical systems
Hammerstein integral equation
Holder condition
Lipschitz condition
Semilocal convergence
MATEMATICA APLICADA
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spelling Recurrence relations for a family of iterations assuming Holder continuous second order Frechet derivativeGupta, Dharmendra KumarSingh, SukhjitHueso, Jose LuisSrivastava, ShwetabhKumar, AbhimanyuMartínez Molada, Eulalia|||0000-0003-2869-4334Dynamical systemsHammerstein integral equationHolder conditionLipschitz conditionSemilocal convergenceMATEMATICA APLICADA[EN] The semilocal convergence using recurrence relations of a family of iterations for solving nonlinear equations in Banach spaces is established. It is done under the assumption that the second order Frechet derivative satisfies the Holder continuity condition. This condition is more general than the usual Lipschitz continuity condition used for this purpose. Examples can be given forwhich the Lipschitz continuity condition fails but the Holder continuity condition works on the second order Frechet derivative. Recurrence relations based on three parameters are derived. A theorem for existence and uniqueness along with the error bounds for the solution is provided. The R-order of convergence is shown to be equal to 3 + q when theta = +/- 1; otherwise it is 2 + q, where q epsilon (0, 1]. Numerical examples involving nonlinear integral equations and boundary value problems are solved and improved convergence balls are found for them. Finally, the dynamical study of the family of iterations is also carried out.Walter de Gruyter GmbHEscuela Técnica Superior de Ingeniería de TelecomunicaciónDepartamento de Matemática AplicadaInstituto Universitario de Matemática MultidisciplinarAGENCIA ESTATAL DE INVESTIGACIONRepositorio Institucional de la Universitat Politècnica de València Riunet20212021-06-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/182191reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PGC2018-095896-B-C22 DISEÑO, ANALISIS Y ESTABILIDAD DE PROCESOS ITERATIVOS APLICADOS A LAS ECUACIONES INTEGRALES Y MATRICIALES Y A LA COMUNICACION AEROESPACIALopen accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1821912026-06-13T07:49:27Z
dc.title.none.fl_str_mv Recurrence relations for a family of iterations assuming Holder continuous second order Frechet derivative
title Recurrence relations for a family of iterations assuming Holder continuous second order Frechet derivative
spellingShingle Recurrence relations for a family of iterations assuming Holder continuous second order Frechet derivative
Gupta, Dharmendra Kumar
Dynamical systems
Hammerstein integral equation
Holder condition
Lipschitz condition
Semilocal convergence
MATEMATICA APLICADA
title_short Recurrence relations for a family of iterations assuming Holder continuous second order Frechet derivative
title_full Recurrence relations for a family of iterations assuming Holder continuous second order Frechet derivative
title_fullStr Recurrence relations for a family of iterations assuming Holder continuous second order Frechet derivative
title_full_unstemmed Recurrence relations for a family of iterations assuming Holder continuous second order Frechet derivative
title_sort Recurrence relations for a family of iterations assuming Holder continuous second order Frechet derivative
dc.creator.none.fl_str_mv Gupta, Dharmendra Kumar
Singh, Sukhjit
Hueso, Jose Luis
Srivastava, Shwetabh
Kumar, Abhimanyu
Martínez Molada, Eulalia|||0000-0003-2869-4334
author Gupta, Dharmendra Kumar
author_facet Gupta, Dharmendra Kumar
Singh, Sukhjit
Hueso, Jose Luis
Srivastava, Shwetabh
Kumar, Abhimanyu
Martínez Molada, Eulalia|||0000-0003-2869-4334
author_role author
author2 Singh, Sukhjit
Hueso, Jose Luis
Srivastava, Shwetabh
Kumar, Abhimanyu
Martínez Molada, Eulalia|||0000-0003-2869-4334
author2_role author
author
author
author
author
dc.contributor.none.fl_str_mv Escuela Técnica Superior de Ingeniería de Telecomunicación
Departamento de Matemática Aplicada
Instituto Universitario de Matemática Multidisciplinar
AGENCIA ESTATAL DE INVESTIGACION
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Dynamical systems
Hammerstein integral equation
Holder condition
Lipschitz condition
Semilocal convergence
MATEMATICA APLICADA
topic Dynamical systems
Hammerstein integral equation
Holder condition
Lipschitz condition
Semilocal convergence
MATEMATICA APLICADA
description [EN] The semilocal convergence using recurrence relations of a family of iterations for solving nonlinear equations in Banach spaces is established. It is done under the assumption that the second order Frechet derivative satisfies the Holder continuity condition. This condition is more general than the usual Lipschitz continuity condition used for this purpose. Examples can be given forwhich the Lipschitz continuity condition fails but the Holder continuity condition works on the second order Frechet derivative. Recurrence relations based on three parameters are derived. A theorem for existence and uniqueness along with the error bounds for the solution is provided. The R-order of convergence is shown to be equal to 3 + q when theta = +/- 1; otherwise it is 2 + q, where q epsilon (0, 1]. Numerical examples involving nonlinear integral equations and boundary value problems are solved and improved convergence balls are found for them. Finally, the dynamical study of the family of iterations is also carried out.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-06-01
dc.type.none.fl_str_mv journal 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://riunet.upv.es/handle/10251/182191
url https://riunet.upv.es/handle/10251/182191
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 http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PGC2018-095896-B-C22 DISEÑO, ANALISIS Y ESTABILIDAD DE PROCESOS ITERATIVOS APLICADOS A LAS ECUACIONES INTEGRALES Y MATRICIALES Y A LA COMUNICACION AEROESPACIAL
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
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
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Walter de Gruyter GmbH
publisher.none.fl_str_mv Walter de Gruyter GmbH
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869420326760218625
score 15,300724

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