${\cal T}$-class algorithms for pseudocontractions and $\kappa$-strict pseudocontractions in Hilbert spaces

TL;DR

This paper explores iterative algorithms for fixed points and variational inequalities involving $eta$-strict pseudocontractions in Hilbert spaces, connecting existing methods within a unified ${ m T}$-class framework.

Contribution

It establishes links between known algorithms for pseudocontractions and the general ${ m T}$-class framework, enhancing theoretical understanding.

Findings

Unified framework for pseudocontraction algorithms

Connections between fixed point and variational inequality solutions

Extension of ${ m T}$-class algorithms to new problem classes

Abstract

In this paper we study iterative algorithms for finding a common element of the set of fixed points of $\kappa$-strict pseudocontractions or finding a solution of a variational inequality problem for a monotone, Lipschitz continuous mapping. The last problem being related to finding fixed points of pseudocontractions. These algorithms were already studied in [G.L. Acedo, H.-K. Xu] and [N. Nadezhkina, W. Takahashi] but our aim here is to provide the links between these know algorithms and the general framework of ${\cal T}$-class algorithms studied in [H.H. Bauschke, P.L. Combettes].