A Totally Relaxed Self-Adaptive Subgradient Extragradient Scheme for Equilibrium and Fixed Point Problems in a Banach Space
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Authors: O. K. OYEWOLE, H. A. ABASS AND O. T. MEWOMO
DOI: 10.46793/KgJMat2502.181O
Abstract:
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.
Keywords:
Equilibrium problem, strongly pseudomonotone, strong convergence, Banach space, quasi-ϕ-nonexpansive mapping, fixed point.
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