The subgradient extragradient method for solving pseudomonotone equilibrium and fixed point problems in Banach spaces

In this paper, we introduce a self-adaptive subgradient extragradient method for finding a common element in the solution set of a pseudomonotone equilibrium problem and set of fixed points of a quasi-phi-nonexpansive mapping in 2-uniformly convex and uniformly smooth Banach spaces. The stepsize of the algorithm is selected self-adaptively which helps to prevent the necessity for prior estimates of the Lipschitz-like constants of the bifunction. A strong convergence result is proved under some mild conditions and some applications to Nash equilibrium problem and contact problem are presented to show the applicability of the result. Furthermore, some numerical examples are given to illustrate the efficiency and accuracy of the proposed method by comparing with other related methods in the literature.