Hybrid Inertial Accelerated Extragradient Algorithms for Split Pseudomonotone Equilibrium Problems and Fixed Point Problems of Demicontractive Mappings

Abstract

In this paper, we present a new hybrid extragradient algorithm for finding a common element of the fixed point problem for a demicontractive mapping and the split equilibrium problem for a pseudomonotone and Lipschitz-type continuous bifunction. By using a new technique of choosing the step size of the proposed method, our algorithms do not need any prior information of the operator norm. In fact, we propose an inertial type algorithm in order to accelerate its convergence rate and then  prove strong convergence theorem of our proposed method under some control conditions. Moreover, we give some numerical experiments to support our main results.