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

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

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dc.contributor.author Gupta, Dharmendra Kumar es_ES
dc.contributor.author Martínez Molada, Eulalia es_ES
dc.contributor.author Singh, Sukhjit es_ES
dc.contributor.author Hueso, Jose Luis es_ES
dc.contributor.author Srivastava, Shwetabh es_ES
dc.contributor.author Kumar, Abhimanyu es_ES
dc.date.accessioned 2022-04-27T10:07:21Z
dc.date.available 2022-04-27T10:07:21Z
dc.date.issued 2021-06-01 es_ES
dc.identifier.issn 1565-1339 es_ES
dc.identifier.uri http://hdl.handle.net/10251/182191
dc.description.abstract [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. es_ES
dc.language Inglés es_ES
dc.publisher Walter de Gruyter GmbH es_ES
dc.relation.ispartof International Journal of Nonlinear Sciences and Numerical Simulation es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Dynamical systems es_ES
dc.subject Hammerstein integral equation es_ES
dc.subject Holder condition es_ES
dc.subject Lipschitz condition es_ES
dc.subject Semilocal convergence es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Recurrence relations for a family of iterations assuming Holder continuous second order Frechet derivative es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1515/ijnsns-2016-0151 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095896-B-C22/ES/DISEÑO, ANALISIS Y ESTABILIDAD DE PROCESOS ITERATIVOS APLICADOS A LAS ECUACIONES INTEGRALES Y MATRICIALES Y A LA COMUNICACION AEROESPACIAL/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Gupta, DK.; Martínez Molada, E.; Singh, S.; Hueso, JL.; Srivastava, S.; Kumar, A. (2021). Recurrence relations for a family of iterations assuming Holder continuous second order Frechet derivative. International Journal of Nonlinear Sciences and Numerical Simulation. 22(3-4):267-285. https://doi.org/10.1515/ijnsns-2016-0151 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1515/ijnsns-2016-0151 es_ES
dc.description.upvformatpinicio 267 es_ES
dc.description.upvformatpfin 285 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 22 es_ES
dc.description.issue 3-4 es_ES
dc.relation.pasarela S\440195 es_ES
dc.contributor.funder AGENCIA ESTATAL DE INVESTIGACION es_ES
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