Extended Local Convergence for the Combined Newton-Kurchatov Method Under the Generalized Lipschitz Conditions

Extended Local Convergence for the Combined Newton-Kurchatov Method Under the Generalized Lipschitz Conditions

We present a local convergence of the combined Newton-Kurchatov method for solving Banach space valued equations. The convergence criteria involve derivatives until the second and Lipschitz-type conditions are satisfied, as well as a new center-Lipschitz-type condition and the notion of the restrict...

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Main Authors: Ioannis K. Argyros, Stepan Shakhno
Format: Article
Language:English
Published: MDPI AG 2019-02-01
Series:Mathematics
Subjects:
nonlinear equation
iterative process
non-differentiable operator
Lipschitz condition
Online Access:https://www.mdpi.com/2227-7390/7/2/207
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spelling doaj-fa75b68d9756409db399ad5c5aa6f8bd2020-11-24T20:47:25ZengMDPI AGMathematics2227-73902019-02-017220710.3390/math7020207math7020207Extended Local Convergence for the Combined Newton-Kurchatov Method Under the Generalized Lipschitz ConditionsIoannis K. Argyros0Stepan Shakhno1Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USADepartment of Theory of Optimal Processes, Ivan Franko National University of Lviv, 79000 Lviv, UkraineWe present a local convergence of the combined Newton-Kurchatov method for solving Banach space valued equations. The convergence criteria involve derivatives until the second and Lipschitz-type conditions are satisfied, as well as a new center-Lipschitz-type condition and the notion of the restricted convergence region. These modifications of earlier conditions result in a tighter convergence analysis and more precise information on the location of the solution. These advantages are obtained under the same computational effort. Using illuminating examples, we further justify the superiority of our new results over earlier ones.https://www.mdpi.com/2227-7390/7/2/207nonlinear equationiterative processnon-differentiable operatorLipschitz condition
collection DOAJ
language English
format Article
sources DOAJ
author Ioannis K. Argyros
Stepan Shakhno
spellingShingle Ioannis K. Argyros
Stepan Shakhno
Extended Local Convergence for the Combined Newton-Kurchatov Method Under the Generalized Lipschitz Conditions
Mathematics
nonlinear equation
iterative process
non-differentiable operator
Lipschitz condition
author_facet Ioannis K. Argyros
Stepan Shakhno
author_sort Ioannis K. Argyros
title Extended Local Convergence for the Combined Newton-Kurchatov Method Under the Generalized Lipschitz Conditions
title_short Extended Local Convergence for the Combined Newton-Kurchatov Method Under the Generalized Lipschitz Conditions
title_full Extended Local Convergence for the Combined Newton-Kurchatov Method Under the Generalized Lipschitz Conditions
title_fullStr Extended Local Convergence for the Combined Newton-Kurchatov Method Under the Generalized Lipschitz Conditions
title_full_unstemmed Extended Local Convergence for the Combined Newton-Kurchatov Method Under the Generalized Lipschitz Conditions
title_sort extended local convergence for the combined newton-kurchatov method under the generalized lipschitz conditions
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2019-02-01
description We present a local convergence of the combined Newton-Kurchatov method for solving Banach space valued equations. The convergence criteria involve derivatives until the second and Lipschitz-type conditions are satisfied, as well as a new center-Lipschitz-type condition and the notion of the restricted convergence region. These modifications of earlier conditions result in a tighter convergence analysis and more precise information on the location of the solution. These advantages are obtained under the same computational effort. Using illuminating examples, we further justify the superiority of our new results over earlier ones.
topic nonlinear equation
iterative process
non-differentiable operator
Lipschitz condition
url https://www.mdpi.com/2227-7390/7/2/207
work_keys_str_mv AT ioanniskargyros extendedlocalconvergenceforthecombinednewtonkurchatovmethodunderthegeneralizedlipschitzconditions
AT stepanshakhno extendedlocalconvergenceforthecombinednewtonkurchatovmethodunderthegeneralizedlipschitzconditions
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