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arXiv · 2307.07337

Strict pseudocontractions and demicontractions, their properties and applications

Andrzej Cegielski
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Abstract

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.

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Andrzej Cegielski. 2023-07-14. Strict pseudocontractions and demicontractions, their properties and applications. https://arxiv.org/abs/2307.07337

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