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Geometrically Constructed Family of the Simple Fixed Point Iteration Method

Author

Listed:
  • Vinay Kanwar

    (University Institute of Engineering and Technology, Panjab University, Chandigarh 160014, India)

  • Puneet Sharma

    (University Institute of Engineering and Technology, Panjab University, Chandigarh 160014, India
    Department of Mathematics, Goswami Ganesh Dutta Sanatan Dharma College, Chandigarh 160030, India)

  • Ioannis K. Argyros

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

  • Ramandeep Behl

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Christopher Argyros

    (Department of Computer Science, University of Oklahoma, Norman, OK 73071, USA)

  • Ali Ahmadian

    (Institute of IR 4.0, The National University of Malaysia, Bangi 43600, UKM, Malaysia)

  • Mehdi Salimi

    (Department of Mathematics & Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada
    Center for Dynamics and Institute for Analysis, Faculty of Mathematics, Technische Universität Dresden, 01062 Dresden, Germany)

Abstract

This study presents a new one-parameter family of the well-known fixed point iteration method for solving nonlinear equations numerically. The proposed family is derived by implementing approximation through a straight line. The presence of an arbitrary parameter in the proposed family improves convergence characteristic of the simple fixed point iteration as it has a wider domain of convergence. Furthermore, we propose many two-step predictor–corrector iterative schemes for finding fixed points, which inherit the advantages of the proposed fixed point iterative schemes. Finally, several examples are given to further illustrate their efficiency.

Suggested Citation

  • Vinay Kanwar & Puneet Sharma & Ioannis K. Argyros & Ramandeep Behl & Christopher Argyros & Ali Ahmadian & Mehdi Salimi, 2021. "Geometrically Constructed Family of the Simple Fixed Point Iteration Method," Mathematics, MDPI, vol. 9(6), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:694-:d:522864
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    References listed on IDEAS

    as
    1. Sharifi, Somayeh & Salimi, Mehdi & Siegmund, Stefan & Lotfi, Taher, 2016. "A new class of optimal four-point methods with convergence order 16 for solving nonlinear equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 119(C), pages 69-90.
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