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

## TL;DR

This paper explores the strong convergence properties of algorithms for finding common fixed points of nonexpansive mappings in Hilbert spaces, linking various iterative methods and extending existing theorems.

## Contribution

It establishes new connections between ${
m T}_C$-class algorithms, CQ Algorithm, and shrinking projection methods, extending convergence results for nonexpansive mappings.

## Key findings

- Strong convergence of algorithms is related to coherent ${
m T}_C$-class sequences.
- Examples demonstrate applicability to nonexpansive finite sets and semigroups.
- Extensions of existing theorems on fixed point convergence.

## Abstract

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