Strong convergence theorems for a nonexpansive mapping and its applications for solving the split feasibility problem

The aim of this paper is to propose some novel algorithms and their strong convergence theorems for solving the split feasibility problem, and we obtain the corresponding strong convergence results under mild conditions. The split feasibility problem was proposed by [Y. Censor, Y. Elfving, Numer. Algorithms, 8 (1994), 221-239]. So far a lot of algorithms have been given for solving this problem due to its applications in intensitymodulated radiation therapy, signal processing, and image reconstruction. But most of these algorithms are of weak convergence. In this paper, we propose the new algorithms which can provide useful guidelines for solving the relevant problem, such as the split common fixed point problem (SCFP), multiset split feasibility problem and so on.