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Convergence Criteria of Three Step Schemes for Solving Equations

Author

Listed:
  • Samundra Regmi

    (Learning Commons, University of North Texas at Dallas, Dallas, TX 75201, USA)

  • Christopher I. Argyros

    (Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA)

  • Ioannis K. Argyros

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

  • Santhosh George

    (Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangalore 575 025, India)

Abstract

We develop a unified convergence analysis of three-step iterative schemes for solving nonlinear Banach space valued equations. The local convergence order has been shown before to be five on the finite dimensional Euclidean space assuming Taylor expansions and the existence of the sixth derivative not on these schemes. So, the usage of them is restricted six or higher differentiable mappings. But in our paper only the first Frèchet derivative is utilized to show convergence. Consequently, the scheme is expanded. Numerical applications are also given to test convergence.

Suggested Citation

  • Samundra Regmi & Christopher I. Argyros & Ioannis K. Argyros & Santhosh George, 2021. "Convergence Criteria of Three Step Schemes for Solving Equations," Mathematics, MDPI, vol. 9(23), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3106-:d:693521
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