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Article

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

1
Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
2
Department of Theory of Optimal Processes, Ivan Franko National University of Lviv, 79000 Lviv, Ukraine
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(2), 207; https://doi.org/10.3390/math7020207
Received: 4 February 2019 / Revised: 19 February 2019 / Accepted: 20 February 2019 / Published: 23 February 2019
(This article belongs to the Special Issue Iterative Methods for Solving Nonlinear Equations and Systems)
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. View Full-Text
Keywords: nonlinear equation; iterative process; non-differentiable operator; Lipschitz condition nonlinear equation; iterative process; non-differentiable operator; Lipschitz condition
MDPI and ACS Style

Argyros, I.K.; Shakhno, S. Extended Local Convergence for the Combined Newton-Kurchatov Method Under the Generalized Lipschitz Conditions. Mathematics 2019, 7, 207. https://doi.org/10.3390/math7020207

AMA Style

Argyros IK, Shakhno S. Extended Local Convergence for the Combined Newton-Kurchatov Method Under the Generalized Lipschitz Conditions. Mathematics. 2019; 7(2):207. https://doi.org/10.3390/math7020207

Chicago/Turabian Style

Argyros, Ioannis K.; Shakhno, Stepan. 2019. "Extended Local Convergence for the Combined Newton-Kurchatov Method Under the Generalized Lipschitz Conditions" Mathematics 7, no. 2: 207. https://doi.org/10.3390/math7020207

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