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Extending the Applicability of a Two-Step Chord-Type Method for Non-Differentiable Operators

Author

Listed:
  • Ioannis K. Argyros

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

  • Neha Gupta

    (Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal 462003, India)

  • J. P. Jaiswal

    (Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal 462003, India)

Abstract

The semi-local convergence analysis of a well defined and efficient two-step Chord-type method in Banach spaces is presented in this study. The recurrence relation technique is used under some weak assumptions. The pertinency of the assumed method is extended for nonlinear non-differentiable operators. The convergence theorem is also established to show the existence and uniqueness of the approximate solution. A numerical illustration is quoted to certify the theoretical part which shows that earlier studies fail if the function is non-differentiable.

Suggested Citation

  • Ioannis K. Argyros & Neha Gupta & J. P. Jaiswal, 2019. "Extending the Applicability of a Two-Step Chord-Type Method for Non-Differentiable Operators," Mathematics, MDPI, vol. 7(9), pages 1-8, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:804-:d:262954
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    References listed on IDEAS

    as
    1. Abhimanyu Kumar & D. K. Gupta & Shwetabh Srivastava, 2017. "Influence of the Center Condition on the Two-Step Secant Method," International Journal of Analysis, Hindawi, vol. 2017, pages 1-9, September.
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