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Unified Convergence Criteria for Iterative Banach Space Valued Methods with Applications

Author

Listed:
  • Ioannis K. Argyros

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

Abstract

A plethora of sufficient convergence criteria has been provided for single-step iterative methods to solve Banach space valued operator equations. However, an interesting question remains unanswered: is it possible to provide unified convergence criteria for single-step iterative methods, which are weaker than earlier ones without additional hypotheses? The answer is yes. In particular, we provide only one sufficient convergence criterion suitable for single-step methods. Moreover, we also give a finer convergence analysis. Numerical experiments involving boundary value problems and Hammerstein-like integral equations complete this paper.

Suggested Citation

  • Ioannis K. Argyros, 2021. "Unified Convergence Criteria for Iterative Banach Space Valued Methods with Applications," Mathematics, MDPI, vol. 9(16), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1942-:d:614386
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    Citations

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    Cited by:

    1. Janak Raj Sharma & Harmandeep Singh & Ioannis K. Argyros, 2022. "A Unified Local-Semilocal Convergence Analysis of Efficient Higher Order Iterative Methods in Banach Spaces," Mathematics, MDPI, vol. 10(17), pages 1-16, September.
    2. Michael I. Argyros & Ioannis K. Argyros & Samundra Regmi & Santhosh George, 2022. "Generalized Three-Step Numerical Methods for Solving Equations in Banach Spaces," Mathematics, MDPI, vol. 10(15), pages 1-28, July.
    3. Ioannis K. Argyros & Samundra Regmi & Stepan Shakhno & Halyna Yarmola, 2022. "A Methodology for Obtaining the Different Convergence Orders of Numerical Method under Weaker Conditions," Mathematics, MDPI, vol. 10(16), pages 1-16, August.
    4. Ioannis K. Argyros & Christopher Argyros & Johan Ceballos & Daniel González, 2022. "Extended Comparative Study between Newton’s and Steffensen-like Methods with Applications," Mathematics, MDPI, vol. 10(16), pages 1-12, August.
    5. Samundra Regmi & Ioannis K. Argyros & Santhosh George & Michael I. Argyros, 2022. "A Comparison Study of the Classical and Modern Results of Semi-Local Convergence of Newton–Kantorovich Iterations-II," Mathematics, MDPI, vol. 10(11), pages 1-12, May.
    6. Santhosh George & Jidesh Padikkal & Krishnendu Remesh & Ioannis K. Argyros, 2022. "A New Parameter Choice Strategy for Lavrentiev Regularization Method for Nonlinear Ill-Posed Equations," Mathematics, MDPI, vol. 10(18), pages 1-24, September.
    7. Manoj K. Singh & Ioannis K. Argyros, 2022. "The Dynamics of a Continuous Newton-like Method," Mathematics, MDPI, vol. 10(19), pages 1-14, October.
    8. Ramandeep Behl & Ioannis K. Argyros & Fouad Othman Mallawi & Samaher Khalaf Alharbi, 2022. "Extending the Applicability of Highly Efficient Iterative Methods for Nonlinear Equations and Their Applications," Mathematics, MDPI, vol. 11(1), pages 1-18, December.
    9. Samundra Regmi & Ioannis K. Argyros & Santhosh George & Christopher I. Argyros, 2022. "A Comparison Study of the Classical and Modern Results of Semi-Local Convergence of Newton-Kantorovich Iterations," Mathematics, MDPI, vol. 10(8), pages 1-14, April.

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