# Strict pseudocontractions and demicontractions, their properties and applications

arXiv: https://arxiv.org/abs/2307.07337 · HTML: https://mlsanity.com/paper/2307.07337/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jul 2023.

## Built on by (most cited first, 1 of 1)

- [A Unified Plug-and-Play Algorithm with Projected Landweber Operator for Split Convex Feasibility Problems](https://mlsanity.com/paper/2408.12100/) (2024)

## Abstract (arXiv)

We give properties of strict pseudocontractions and demicontractions defined on a Hilbert space, which constitute wide classes of operators that arise in iterative methods for solving fixed point problems. In particular, we give necessary and sufficient conditions under which a convex combination and composition of strict pseudocontractions as well as demicontractions that share a common fixed point is again a strict pseudocontraction or a demicontraction, respectively. Moreover, we introduce a generalized relaxation of composition of demicontraction and give its properties. We apply these properties to prove the weak convergence of a class of algorithms that is wider than the Douglas-Rachford algorithm and projected Landweber algorithms. We have also presented two numerical examples, where we compare the behavior of the presented methods with the Douglas-Rachford method.