Inertial extragradient and Ishikawa iterative methods for approximating common solutions to pseudomonotone equilibrium problems and fixed points of quasinonexpansive operators

In this paper, two new algorithms are introduced for finding a common point of the solution set of a class of equilibrium problems involving pseudomonotone bifunctions and satisfying the Lipschitz-type condition and the set of fixed points of a quasinonexpansive in a real Hilbert space.This algorithms can be considered as a combination of the extragradient method with inertial effects for equilibrium problems and the Ishikawa method for fixed point problems.Strong and weak convergence of the proposed algorithms are established under some mild assumptions.Some numerical examples are implemented to show the computational efficiency of the proposed algorithms.