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 derivative Gupta, Dharmendra Kumar Singh, Sukhjit Hueso, Jose Luis Srivastava, Shwetabh Kumar, Abhimanyu Martínez Molada, Eulalia|||0000-0003-2869-4334 Dynamical systems Hammerstein integral equation Holder condition Lipschitz condition Semilocal convergence MATEMATICA 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 GmbH https://riunet.upv.es/handle/10251/182191
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
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
topic Dynamical systems
Hammerstein integral equation
Holder condition
Lipschitz condition
Semilocal convergence
MATEMATICA APLICADA
topic_facet 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
format article
url https://riunet.upv.es/handle/10251/182191
language eng
eu_rights_str_mv openAccess
publisher Walter de Gruyter GmbH
institution Universitat Politècnica de València (UPV)
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname_str Universitat Politècnica de València (UPV)
_version_ 1878441144416731137
publishDateSort 2021
author_browse Gupta, Dharmendra Kumar
Hueso, Jose Luis
Kumar, Abhimanyu
Martínez Molada, Eulalia|||0000-0003-2869-4334
Singh, Sukhjit
Srivastava, Shwetabh
publisherStr Walter de Gruyter GmbH
score 6,9303427

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