Shrinking Inertial Extragradient Methods for Solving Split Equilibrium and Fixed Point Problems

Narin Petrot, Manatchanok Khonchaliew

Abstract

This paper presents two shrinking inertial extragradient algorithms for finding a solution of the split equilibrium and fixed point problems involving nonexpansive mappings and pseudomonotone bifunctions that satisfy Lipschitz-type continuous in the setting of real Hilbert spaces. The strong convergence theorems of the introduced algorithms are showed either with or without the prior knowledge of the Lipschitz-type constants of bifunctions under some constraint qualifications of the scalar sequences. Some numerical experiments are  performed  to demonstrate  the computational effectiveness of the established algorithms.