Strong convergence theorems for equilibrium problems and fixed point problems in Banach spaces

The paper proposes two new iterative methods for solving pseudomonotone equilibrium problems involving fixed point problems for quasi-$$\phi $$ϕ-nonexpansive mappings in Banach spaces. The proposed algorithms combine the extended extragradient method or the linesearch method with the Halpern iteration. The strong convergence theorems are established under standard assumptions imposed on equilibrium bifunctions and mappings. The results in this paper have generalized and enriched existing algorithms for equilibrium problems in Banach spaces.

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