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Semilocal Convergence Analysis of S-iteration Process of Newton–Kantorovich Like in Banach Spaces

Author

Listed:
  • Daya Ram Sahu

    (Banaras Hindu University)

  • Jen Chih Yao

    (China Medical University
    King Abdulaziz University)

  • Vipin Kumar Singh

    (Banaras Hindu University)

  • Satyendra Kumar

    (Banaras Hindu University)

Abstract

In the present article, we establish a semilocal convergence theorem for the S-iteration process of Newton–Kantorovich like in Banach space setting for solving nonlinear operator equations and discuss its semilocal convergence analysis. We apply our result to solve the Fredholm-integral equations.

Suggested Citation

  • Daya Ram Sahu & Jen Chih Yao & Vipin Kumar Singh & Satyendra Kumar, 2017. "Semilocal Convergence Analysis of S-iteration Process of Newton–Kantorovich Like in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 102-127, January.
    • Handle: RePEc:spr:joptap:v:172:y:2017:i:1:d:10.1007_s10957-016-1031-x
    DOI: 10.1007/s10957-016-1031-x
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    References listed on IDEAS

    as
    1. M. Chen & Y. Khan & Q. Wu & A. Yildirim, 2013. "Newton–Kantorovich Convergence Theorem of a Modified Newton’s Method Under the Gamma-Condition in a Banach Space," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 651-662, June.
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    Cited by:

    1. Singh, Vipin Kumar, 2020. "On the convergence of inexact Newton-like methods under mild differentiability conditions," Applied Mathematics and Computation, Elsevier, vol. 370(C).

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