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A Unified Convergence Analysis for Some Two-Point Type Methods for Nonsmooth Operators

Author

Listed:
  • Sergio Amat

    (Departamentode Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, 11003 Cádiz, Spain
    These authors contributed equally to this work.)

  • Ioannis Argyros

    (Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
    These authors contributed equally to this work.)

  • Sonia Busquier

    (Departamentode Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, 11003 Cádiz, Spain
    These authors contributed equally to this work.)

  • Miguel Ángel Hernández-Verón

    (Departamento de Matemáticas y Computación, Universidad de La Rioja, Calle Madre de Dios, 53, 26006 Logrono, Spain
    These authors contributed equally to this work.)

  • María Jesús Rubio

    (Departamento de Matemáticas y Computación, Universidad de La Rioja, Calle Madre de Dios, 53, 26006 Logrono, Spain
    These authors contributed equally to this work.)

Abstract

The aim of this paper is the approximation of nonlinear equations using iterative methods. We present a unified convergence analysis for some two-point type methods. This way we compare specializations of our method using not necessarily the same convergence criteria. We consider both semilocal and local analysis. In the first one, the hypotheses are imposed on the initial guess and in the second on the solution. The results can be applied for smooth and nonsmooth operators.

Suggested Citation

  • Sergio Amat & Ioannis Argyros & Sonia Busquier & Miguel Ángel Hernández-Verón & María Jesús Rubio, 2019. "A Unified Convergence Analysis for Some Two-Point Type Methods for Nonsmooth Operators," Mathematics, MDPI, vol. 7(8), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:701-:d:254616
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    Cited by:

    1. Petko D. Proinov & Milena D. Petkova, 2021. "On the Convergence of a New Family of Multi-Point Ehrlich-Type Iterative Methods for Polynomial Zeros," Mathematics, MDPI, vol. 9(14), pages 1-16, July.

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