Halpern-Subgradient Extragradient Method for Solving Equilibrium and Common Fixed Point Problems in Reflexive Banach Spaces

Annel Thembinkosi Bokodisa, Lateef Olakunle Jolaoso and Maggie Aphane
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Annel Thembinkosi Bokodisa: Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94, Medunsa 0204, Pretoria, South Africa
Lateef Olakunle Jolaoso: Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94, Medunsa 0204, Pretoria, South Africa
Maggie Aphane: Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94, Medunsa 0204, Pretoria, South Africa

Mathematics, 2021, vol. 9, issue 7, 1-24

Abstract: In this paper, using the concept of Bregman distance, we introduce a new Bregman subgradient extragradient method for solving equilibrium and common fixed point problems in a real reflexive Banach space. The algorithm is designed, such that the stepsize is chosen without prior knowledge of the Lipschitz constants. We also prove a strong convergence result for the sequence that is generated by our algorithm under mild conditions. We apply our result to solving variational inequality problems, and finally, we give some numerical examples to illustrate the efficiency and accuracy of the algorithm.

Keywords: equilibrium problem; pseudomonotone; Bregman distance; real reflexive Banach space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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