Inertial-based extragradient algorithm for approximating a common solution of split-equilibrium problems and fixed-point problems of nonexpansive semigroups

In this paper, we introduce a simple and easily computable algorithm for finding a common solution to split-equilibrium problems and fixed-point problems in the framework of real Hilbert spaces. New self-adaptive step sizes are adopted for the avoidance of Lipschitz constants that are not practically implemented. Furthermore, an inertial term is incorporated to speed up the rate of convergence, a condition that is very desirable in applications. A strong convergence is obtained under some mild assumptions, which is not limited to the fact that the bifunctions are pseudomonotone operators. This condition is better, weaker, and more general than being strongly pseudomonotone or monotone. Our result improves and extends already announced results in this direction of research.