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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Bibliographic Details
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
Description
Summary: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.
ISSN:2227-7390

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