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

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