An accelerated hybrid projection method with a self-adaptive step-size sequence for solving split common fixed point problems

Abstract

This paper attempts to solve the split common fixed point problem for demicontractive mappings. We give an accelerated hybrid projection algorithm that combines the hybrid projection method and the inertial technique. The strong convergence theorem of this algorithm is obtained under mild conditions by a self-adaptive step-size sequence, which does not need prior knowledge of the operator norm. Some numerical experiments in infinite-dimensional Hilbert spaces are provided to illustrate the reliability and robustness of the algorithm and also to compare it with existing ones.