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

Author

Listed:
  • Ioannis K. Argyros

    (Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA)

  • Stepan Shakhno

    (Department of Theory of Optimal Processes, Ivan Franko National University of Lviv, 79000 Lviv, Ukraine)

Abstract

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.

Suggested Citation

  • Ioannis K. Argyros & Stepan Shakhno, 2019. "Extended Local Convergence for the Combined Newton-Kurchatov Method Under the Generalized Lipschitz Conditions," Mathematics, MDPI, vol. 7(2), pages 1-12, February.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:207-:d:208594
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    Cited by:

    1. Chein-Shan Liu & Chung-Lun Kuo & Chih-Wen Chang, 2023. "Regularized Normalization Methods for Solving Linear and Nonlinear Eigenvalue Problems," Mathematics, MDPI, vol. 11(18), pages 1-24, September.
    2. Chein-Shan Liu & Chih-Wen Chang, 2024. "New Memory-Updating Methods in Two-Step Newton’s Variants for Solving Nonlinear Equations with High Efficiency Index," Mathematics, MDPI, vol. 12(4), pages 1-22, February.

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