Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ON M-ITERATIVE SCHEME FOR MAPPINGS WITH ENRICHED (C) CONDITION IN BANACH SPACES

  • Junaid Ahmad (Department of Mathematics and Statistics, International Islamic University)
  • Received : 2023.09.28
  • Accepted : 2024.06.29
  • Published : 2024.12.20
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Abstract

In this paper, we approximate fixed points of mappings satisfying enriched (C) condition under a modified three-step M-iterative scheme in a Banach space setting. First, we establish a weak convergence theorem and then obtain several strong convergence theorems for our iterative scheme under some mild conditions. A numerical example of mappings satisfying enriched (C) condition is used that does not satisfy the ordinary (C) condition to support our main outcome. Numerical computations and graphs obtained from different iterative schemes show that the studied scheme provides a better rate of convergence as compared to some other schemes of the literature. As an application of our main result, we provide a projection type iterative scheme for solving split feasibility problems (SFP) on a Hilbert space setting.

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Acknowledgement

The author would like to thank the unknown reviewers for useful suggestions that improved the first version of the paper.

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