Two-step inertial accelerated algorithms for solving split feasibility problem with multiple output sets

In this paper, we present and study two new two-step inertial accelerated algorithms for finding an approximate solution of split feasibility problems with multiple output sets. Our methods are extensions of CQ algorithms previously studied in the literature. In contrast to the related iterative methods for solving SFP, our methods incorporate a two-step inertial technique that speeds up the convergence rate of the generated sequences to the unique solution of SFP studied in this work. Furthermore, we present weak and strong convergence results where the strong convergence result of our method is obtained without the on-line rule, a feature absent in related algorithms in the literature. Finally, we demonstrate the applicability and performance of our algorithms through numerical experiments. Our numerical results reveal that our methods perform better than existing related methods in the literature.