Domain of Existence and Uniqueness for Nonlinear Hammerstein Integral Equations

[EN] In this work, we performed an study about the domain of existence and uniqueness for an efficient fifth order iterative method for solving nonlinear problems treated in their infinite dimensional form. The hypotheses for the operator and starting guess are weaker than in the previous studies. W...

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Autores: Singh, Sukhjit, Kumar, Abhimanyu, Gupta, D. K., Martínez Molada, Eulalia|||0000-0003-2869-4334
Tipo de recurso: artículo
Fecha de publicación:2020
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:10251/162244
Acceso en línea:https://riunet.upv.es/handle/10251/162244
Access Level:acceso abierto
Palabra clave:Semilocal convergence
Lipschitz condition
Holder condition
Hammerstein integral equation
Dynamical systems
MATEMATICA APLICADA
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spelling Domain of Existence and Uniqueness for Nonlinear Hammerstein Integral EquationsSingh, SukhjitKumar, AbhimanyuGupta, D. K.Martínez Molada, Eulalia|||0000-0003-2869-4334Semilocal convergenceLipschitz conditionHolder conditionHammerstein integral equationDynamical systemsMATEMATICA APLICADA[EN] In this work, we performed an study about the domain of existence and uniqueness for an efficient fifth order iterative method for solving nonlinear problems treated in their infinite dimensional form. The hypotheses for the operator and starting guess are weaker than in the previous studies. We assume omega continuity condition on second order Frechet derivative. This fact it is motivated by showing different problems where the nonlinear operators that define the equation do not verify Lipschitz and Holder condition; however, these operators verify the omega condition established. Then, the semilocal convergence balls are obtained and the R-order of convergence and error bounds can be obtained by following thee main theorem. Finally, we perform a numerical experience by solving a nonlinear Hammerstein integral equations in order to show the applicability of the theoretical results by obtaining the existence and uniqueness balls.This research was partially supported by Ministerio de Economia y Competitividad under grant PGC2018-095896-B-C22.MDPI AGEscuela Técnica Superior de Ingeniería de TelecomunicaciónDepartamento de Matemática AplicadaInstituto Universitario de Matemática MultidisciplinarAgencia Estatal de InvestigaciónRepositorio Institucional de la Universitat Politècnica de València Riunet20202020-03-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/162244reponame: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_abf2Reconocimiento (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1622442026-06-13T07:49:27Z
dc.title.none.fl_str_mv Domain of Existence and Uniqueness for Nonlinear Hammerstein Integral Equations
title Domain of Existence and Uniqueness for Nonlinear Hammerstein Integral Equations
spellingShingle Domain of Existence and Uniqueness for Nonlinear Hammerstein Integral Equations
Singh, Sukhjit
Semilocal convergence
Lipschitz condition
Holder condition
Hammerstein integral equation
Dynamical systems
MATEMATICA APLICADA
title_short Domain of Existence and Uniqueness for Nonlinear Hammerstein Integral Equations
title_full Domain of Existence and Uniqueness for Nonlinear Hammerstein Integral Equations
title_fullStr Domain of Existence and Uniqueness for Nonlinear Hammerstein Integral Equations
title_full_unstemmed Domain of Existence and Uniqueness for Nonlinear Hammerstein Integral Equations
title_sort Domain of Existence and Uniqueness for Nonlinear Hammerstein Integral Equations
dc.creator.none.fl_str_mv Singh, Sukhjit
Kumar, Abhimanyu
Gupta, D. K.
Martínez Molada, Eulalia|||0000-0003-2869-4334
author Singh, Sukhjit
author_facet Singh, Sukhjit
Kumar, Abhimanyu
Gupta, D. K.
Martínez Molada, Eulalia|||0000-0003-2869-4334
author_role author
author2 Kumar, Abhimanyu
Gupta, D. K.
Martínez Molada, Eulalia|||0000-0003-2869-4334
author2_role 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 Investigación
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Semilocal convergence
Lipschitz condition
Holder condition
Hammerstein integral equation
Dynamical systems
MATEMATICA APLICADA
topic Semilocal convergence
Lipschitz condition
Holder condition
Hammerstein integral equation
Dynamical systems
MATEMATICA APLICADA
description [EN] In this work, we performed an study about the domain of existence and uniqueness for an efficient fifth order iterative method for solving nonlinear problems treated in their infinite dimensional form. The hypotheses for the operator and starting guess are weaker than in the previous studies. We assume omega continuity condition on second order Frechet derivative. This fact it is motivated by showing different problems where the nonlinear operators that define the equation do not verify Lipschitz and Holder condition; however, these operators verify the omega condition established. Then, the semilocal convergence balls are obtained and the R-order of convergence and error bounds can be obtained by following thee main theorem. Finally, we perform a numerical experience by solving a nonlinear Hammerstein integral equations in order to show the applicability of the theoretical results by obtaining the existence and uniqueness balls.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-03-01
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/10251/162244
url https://riunet.upv.es/handle/10251/162244
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
Reconocimiento (by)
http://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
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv MDPI AG
publisher.none.fl_str_mv MDPI AG
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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