Two strongly convergent algorithms with momentum for the split common fixed point problems without priori knowledge of operator norms and an application to signal processing

Abstract

Two novel iterative algorithms are proposed for solving the split common fixed point problem with demicontractive operators. Strong convergence theorems of the proposed algorithms are proved. The step-sizes of our algorithms are chosen such that they do not depend on operator norms. The main results proven in this paper extend and improve some results in the literature.  Finally, an application to the signal processing problem is presented  to demonstrate the efficiency of our proposed algorithms.