Strong convergence algorithms for split common fixed point problems involving demicontractive mappings

Abstract

We propose two novel iterative algorithms for solving the split common fixed point problem (SCFPP) involving demicontractive mappings. These algorithms incorporate the inertial technique, which significantly enhances the convergence rate without requiring prior knowledge of operator norms. By eliminating the dependency on operator norms, our methods offer greater flexibility and computational efficiency, making them suitable for large-scale applications. We establish the strong convergence of the proposed algorithms under mild assumptions. Our work extends and generalizes existing results by considering a broader class of mappings and providing a unified framework for solving SCFPPs.