Convergence of an Iteration of Fifth-Order Using Weaker Conditions on First Order Fréchet Derivative in Banach Spaces

[EN] The convergence analysis both local under weaker Argyros-type conditions and semilocal under. omega-condition is established using first order Frechet derivative for an iteration of fifth order in Banach spaces. This avoids derivatives of higher orders which are either difficult to compute or d...

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Autores: Singh, Sukhjit, Gupta, D.K., Singh, R., Singh, M., Martínez Molada, Eulalia|||0000-0003-2869-4334
Formato: artículo
Fecha de publicación:2018
País:España
Recursos:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/121062
Acesso em linha:https://riunet.upv.es/handle/10251/121062
Access Level:acceso abierto
Palavra-chave:Local convergence
Semilocal convergence
Hammerstein-type integral equation
Argyros-type conditions
Frechet derivative
MATEMATICA APLICADA
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spelling Convergence of an Iteration of Fifth-Order Using Weaker Conditions on First Order Fréchet Derivative in Banach SpacesSingh, SukhjitGupta, D.K.Singh, R.Singh, M.Martínez Molada, Eulalia|||0000-0003-2869-4334Local convergenceSemilocal convergenceHammerstein-type integral equationArgyros-type conditionsFrechet derivativeMATEMATICA APLICADA[EN] The convergence analysis both local under weaker Argyros-type conditions and semilocal under. omega-condition is established using first order Frechet derivative for an iteration of fifth order in Banach spaces. This avoids derivatives of higher orders which are either difficult to compute or do not exist at times. The Lipchitz and the Holder conditions are particular cases of the omega-condition. Examples can be constructed for which the Lipchitz and Holder conditions fail but the omega-condition holds. Recurrence relations are used for the semilocal convergence analysis. Existence and uniqueness theorems and the error bounds for the solution are provided. Different examples are solved and convergence balls for each of them are obtained. These examples include Hammerstein-type integrals to demonstrate the applicability of our approach.World ScientificEscuela Técnica Superior de Ingeniería de TelecomunicaciónDepartamento de Matemática AplicadaInstituto Universitario de Matemática MultidisciplinarRepositorio Institucional de la Universitat Politècnica de València Riunet20182018-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/121062reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)Inglésengopen 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:10251/1210622026-06-13T07:49:27Z
dc.title.none.fl_str_mv Convergence of an Iteration of Fifth-Order Using Weaker Conditions on First Order Fréchet Derivative in Banach Spaces
title Convergence of an Iteration of Fifth-Order Using Weaker Conditions on First Order Fréchet Derivative in Banach Spaces
spellingShingle Convergence of an Iteration of Fifth-Order Using Weaker Conditions on First Order Fréchet Derivative in Banach Spaces
Singh, Sukhjit
Local convergence
Semilocal convergence
Hammerstein-type integral equation
Argyros-type conditions
Frechet derivative
MATEMATICA APLICADA
title_short Convergence of an Iteration of Fifth-Order Using Weaker Conditions on First Order Fréchet Derivative in Banach Spaces
title_full Convergence of an Iteration of Fifth-Order Using Weaker Conditions on First Order Fréchet Derivative in Banach Spaces
title_fullStr Convergence of an Iteration of Fifth-Order Using Weaker Conditions on First Order Fréchet Derivative in Banach Spaces
title_full_unstemmed Convergence of an Iteration of Fifth-Order Using Weaker Conditions on First Order Fréchet Derivative in Banach Spaces
title_sort Convergence of an Iteration of Fifth-Order Using Weaker Conditions on First Order Fréchet Derivative in Banach Spaces
dc.creator.none.fl_str_mv Singh, Sukhjit
Gupta, D.K.
Singh, R.
Singh, M.
Martínez Molada, Eulalia|||0000-0003-2869-4334
author Singh, Sukhjit
author_facet Singh, Sukhjit
Gupta, D.K.
Singh, R.
Singh, M.
Martínez Molada, Eulalia|||0000-0003-2869-4334
author_role author
author2 Gupta, D.K.
Singh, R.
Singh, M.
Martínez Molada, Eulalia|||0000-0003-2869-4334
author2_role 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
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Local convergence
Semilocal convergence
Hammerstein-type integral equation
Argyros-type conditions
Frechet derivative
MATEMATICA APLICADA
topic Local convergence
Semilocal convergence
Hammerstein-type integral equation
Argyros-type conditions
Frechet derivative
MATEMATICA APLICADA
description [EN] The convergence analysis both local under weaker Argyros-type conditions and semilocal under. omega-condition is established using first order Frechet derivative for an iteration of fifth order in Banach spaces. This avoids derivatives of higher orders which are either difficult to compute or do not exist at times. The Lipchitz and the Holder conditions are particular cases of the omega-condition. Examples can be constructed for which the Lipchitz and Holder conditions fail but the omega-condition holds. Recurrence relations are used for the semilocal convergence analysis. Existence and uniqueness theorems and the error bounds for the solution are provided. Different examples are solved and convergence balls for each of them are obtained. These examples include Hammerstein-type integrals to demonstrate the applicability of our approach.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-01-01
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/10251/121062
url https://riunet.upv.es/handle/10251/121062
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
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
application/pdf
dc.publisher.none.fl_str_mv World Scientific
publisher.none.fl_str_mv World Scientific
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
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score 15,300724

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