A note on strong convergence to common fixed points of nonexpansive mappings in Hilbert spaces

Abstract

The aim of this paper is to investigate the links between ${\mathcal{T}}_C$-class algorithms, CQ Algorithm and shrinking projection methods. We show that strong convergence of these algorithms are related to coherent ${\mathcal{T}}_C$-class sequences of mapping. Some examples dealing with nonexpansive finite set of mappings and nonexpansive semigroups are given. They extend some existing theorems.