Hybrid Inertial Self-Adaptive Iterative Methods for Split Variational Inclusion Problems

Abstract

Herein, we present two hybrid inertial self-adaptive iterative methods for determining the combined solution of the split variational inclusions and fixed-point problems. Our methods include viscosity approximation, fixed-point iteration, and inertial extrapolation in the initial step of each iteration. We employ two self-adaptive step sizes to compute the iterative sequence, which do not require the pre-calculated norm of a bounded linear operator. We prove strong convergence theorems to approximate the common solution of the split variational inclusions and fixed-point problems. Further, we implement our methods and results to examine split variational inequality and split common fixed-point problems. Finally, we illustrate our methods and compare them with some known methods existing in the literature.