Algorithms for nonexpansive self-mappings with application to the constrained multiple-set split convex feasibility fixed point problem in Hilbert spaces

Abstract

In this article we devise two iteration schemes for approximating common fixed points of a finite family of nonexpansive mappings and establish the corresponding strong convergence theorem for the sequence generated by any one of our algorithms. Then we apply our results to approximate a solution of the so-called constrained multiple-set convex feasibility fixed point problem for firmly nonexpansive mappings which covers the multiple-set convex feasibility problem in the literature. In particular, our algorithms can be used to approximate the zero point problem of maximal monotone operators, and the equilibrium problem. Furthermore, the unique minimum norm solution can be obtained through our algorithms for each mentioned problem.