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

Abstract

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 intensity-modulated 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), multi-set split feasibility problem and so on.

Strong convergence of a new iterative algorithm for fixed points of asymptotically nonexpansive mappings

“…When ξ n = 1 2 , and T is a nonexpansive mapping, Theorem 3.1 can be reduced to the main result of Xu (see [19]). When ξ n = 1, and T is a nonexpansive mapping, Theorem 3.1 can be reduced to the main result of Fan et al (see [3]). …”