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An Adapted Proximal Point Algorithm Utilizing the Golden Ratio Technique for Solving Equilibrium Problems in Banach Spaces

Author

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  • Hammed Anuoluwapo Abass

    (Department of Mathematics and Applied Mathematics, Sefako Makgato Health Science University, Pretoria 0204, South Africa)

  • Olawale Kazeem Oyewole

    (Department of Mathematics and Statistics, Tshwane University of Technology, Arcadia, Pretoria 0007, South Africa)

  • Seithuti Philemon Moshokoa

    (Department of Mathematics and Statistics, Tshwane University of Technology, Arcadia, Pretoria 0007, South Africa)

  • Abubakar Adamu

    (Operational Research Center in Healthcare, Near East University, TRNC Mersin 10, Nicosia 99138, Turkey
    Charles Chidume Mathematics Institute, African University of Science and Technology, Abuja 900107, Nigeria)

Abstract

This paper explores the iterative approximation of solutions to equilibrium problems and proposes a simple proximal point method for addressing them. We incorporate the golden ratio technique as an extrapolation method, resulting in a two-step iterative process. This method is self-adaptive and does not require any Lipschitz-type conditions for implementation. We present and prove a weak convergence theorem along with a sublinear convergence rate for our method. The results extend some previously published findings from Hilbert spaces to 2-uniformly convex Banach spaces. To demonstrate the effectiveness of the method, we provide several numerical illustrations and compare the results with those from other methods available in the literature.

Suggested Citation

  • Hammed Anuoluwapo Abass & Olawale Kazeem Oyewole & Seithuti Philemon Moshokoa & Abubakar Adamu, 2024. "An Adapted Proximal Point Algorithm Utilizing the Golden Ratio Technique for Solving Equilibrium Problems in Banach Spaces," Mathematics, MDPI, vol. 12(23), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3773-:d:1533233
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    References listed on IDEAS

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    1. Nakajo, Kazuhide, 2015. "Strong convergence for gradient projection method and relatively nonexpansive mappings in Banach spaces," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 251-258.
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