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

Hammed Anuoluwapo Abass, Olawale Kazeem Oyewole (), Seithuti Philemon Moshokoa and Abubakar Adamu
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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

Mathematics, 2024, vol. 12, issue 23, 1-17

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.

Keywords: variational inequalities; golden ration technique; Lyapunov function; banach space; self-adaptive stepsize (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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