Halpern-type splitting algorithm for approximating a common solution of monotone inclusion problems and equilibrium problems in reflexive Banach spaces

Abstract

In this paper, we mainly introduce a Halpern-type splitting algorithm with inertial extrapolation for approximating a common solution of monotone inclusion problems and equilibrium problems in reflexive Banach spaces. Our algorithm has a novel step-size rule which is designed by the golden ratio $(\sqrt{5}+1)/2$. The strong convergence results for the proposed algorithm are established under some reasonable assumptions imposed on the operators and the parameters. Furthermore, we give two interesting corollaries based on this algorithm. Finally, several numerical experiments are presented to demonstrate the efficiency and advantages of our proposed algorithm. The results obtained in this paper improve and generalize many recent ones in the literature.