Strong Convergence Theorem Involving Two-Step Inertial Technique Without On-Line Rule for Split Feasibility Problem

Abstract

This work presents an approach for solving the split feasibility problem in an efficient manner. For solving the split feasibility problem, we present a method with a two-step inertial extrapolation and self-adaptive stepsize. The adjustable stepsize and two-step inertial extrapolation both contribute to the proposed method’s improved rate of convergence and decreased computational complexity. The strong convergence results are obtained without on-line rule of the inertial parameters and the iterates. This makes our proof arguments different from what is obtainable in the literature where online rule is imposed on algorithms involving inertial extrapolation step. As far as we know, no strong convergence result has been obtained before now for algorithms with two step inertial for solving split feasibility problems in the literature. To demonstrate the viability of our suggested strategy, numerical results are provided at the end.