Geodesic
A Totally Relaxed Self-Adaptive Subgradient Extragradient Scheme for Equilibrium and Fixed Point Problems in a Banach Space
Kragujevac Journal of Mathematics, Tome 49 (2025) no. 2, p. 181

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The goal of this paper is to introduce a Totally Relaxed Self adaptive Subgradient Extragradient Method (TRSSEM) together with an Halpern iterative method for approximating a common solution of Fixed Point Problem (FPP) and Equilibrium Problem (EP) in 2-uniformly convex and uniformly smooth Banach space. We prove the strong convergence of the sequence generated by our proposed method. The proposed method does not require the computation of a projection onto a feasible set, it instead requires a projection onto a finite intersection of sub-level sets of convex functions. Our result generalizes, unifies and extends some related results in the literature.
Classification : 47H09, 49J35, 90C47
Keywords: equilibrium problem, strongly pseudomonotone, strong convergence, Banach space, quasi-ϕ-nonexpansive mapping, fixed point 
Olawale Kazeem Oyewole; Hammed Anuoluwapo Abass; Oluwatosin Temitope Mewomo. A Totally Relaxed Self-Adaptive Subgradient Extragradient Scheme for Equilibrium and Fixed Point Problems in a Banach Space. Kragujevac Journal of Mathematics, Tome 49 (2025) no. 2, p. 181 . http://geodesic.mathdoc.fr/item/KJM_2025_49_2_a1/
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