Inertial-Based Extragradient Algorithm for Approximating a Common Solution of Split Equilibrium Problems and Fixed Point Problems of Nonexpansive Semigroup

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Abstract In this paper, we introduce a simple and easily computable algorithm for finding a common solution of split eqilibrium problems and fixed point problems in the framework of a real Hilbert space. New self-adaptive stepsizes are adopted for the avoidance of Lipschitz constants that are not practically implemented. Futhermore, inertial term is incorporated to speed up the rate of convergence, a condition which 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 pseu-domonotone operators. This condition is quite better, weaker and more general than being strongly pseudomonotone or monotone. Our result improves and extends already announced results in this direction of research.

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