A Totally Relaxed Self-Adaptive Subgradient Extragradient Scheme for Equilibrium and Fixed Point Problems in a Banach Space

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 s...

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Bibliographic Details
Published in:Kragujevac Journal of Mathematics 2025, Vol.49 (2), p.181-202
Main Authors: OYEWOLE, OLAWALE KAZEEM, ABASS, HAMMED ANUOLUWAPO, MEWOMO, OLUWATOSIN TEMITOPE
Format: Article
Language:English
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Summary: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.
ISSN:1450-9628
2406-3045
DOI:10.46793/KgJMat2502.181O