Inertial Self-Adaptive Viscosity Algorithm for Common Solution of Split Mixed Equilibrium, Split Variational Inclusion and Fixed Point Problems

Abstract

This study aims to propose a self-adaptive viscosity-type algorithm with inertial effects to find the common solutions of the split mixed equilibrium, split variational inclusion and common fixed point problems associated with nonexpansive mappings. It is worth mentioning that the step size employed in this algorithm is independent of the operator norm. Strong convergence of the sequence defined by the proposed algorithm is established. As a consequence, the proposed method can be employed to approximate solutions of the split minimization, split common null point and split feasibility problems. The efficiency of the proposed algorithm is validated by a numerical example and its performance is illustrated by graphical comparisons relative to various established methods presented in recent literature.