Modified inertial extragradient algorithm with non-monotonic step sizes for pseudomonotone equilibrium problems and quasi-nonexpansive mapping

In this paper, we introduce a modified inertial extragradient algorithm with non-monotonic step sizes for approximating a common solution of the pseudomonotone equilibrium problem and the fixed point problem for the quasi-nonexpansive mapping in the framework of a real Hilbert space. Under some constraint qualifications of the scalar sequences, the strong convergence theorem of the introduced algorithm is presented by using the self-adaptive non-monotonic step size without prior information about the Lipschitz constants of bifunction. Some numerical experiments are provided to demonstrate the computational efficiency and advantages of the proposed algorithm.