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A New Modified Fixed-Point Iteration Process

Author

Listed:
  • Chanchal Garodia

    (Department of Mathematics, Jamia Millia Islamia, New Delhi 110025, India)

  • Afrah A. N. Abdou

    (Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Mathematics, Faculty of Sciences, University of Jeddah, Jeddah 23218, Saudi Arabia)

  • Izhar Uddin

    (Department of Mathematics, Jamia Millia Islamia, New Delhi 110025, India)

Abstract

In this paper, we present a new modified iteration process in the setting of uniformly convex Banach space. The newly obtained iteration process can be used to approximate a common fixed point of three nonexpansive mappings. We have obtained strong and weak convergence results for three nonexpansive mappings. Additionally, we have provided an example to support the theoretical proof. In the process, several relevant results are improved and generalized.

Suggested Citation

  • Chanchal Garodia & Afrah A. N. Abdou & Izhar Uddin, 2021. "A New Modified Fixed-Point Iteration Process," Mathematics, MDPI, vol. 9(23), pages 1-10, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3109-:d:693732
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    References listed on IDEAS

    as
    1. Thakur, Balwant Singh & Thakur, Dipti & Postolache, Mihai, 2016. "A new iterative scheme for numerical reckoning fixed points of Suzuki’s generalized nonexpansive mappings," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 147-155.
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