Novel regularized dynamical systems for solving hierarchical fixed point problems

In this paper, we study some Krasnoselskii-Mann type dynamical systems in solving fixed point problems. The first one can be regarded as a continuous version of the Krasnoselskii-Mann iterations. We prove that the solution of this dynamical system converges weakly to a fixed point of the involving m...

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Bibliographic Details
Published in:Dynamical systems (London, England) England), 2024-04, Vol.39 (2), p.268-281
Main Author: Hai, Trinh Ngoc
Format: Article
Language:English
Subjects:
Convergence
Dynamical system
Dynamical systems
fixed point problems
Krasnoselskii-Mann theorem
regularized methods
variational inequalities
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Summary:In this paper, we study some Krasnoselskii-Mann type dynamical systems in solving fixed point problems. The first one can be regarded as a continuous version of the Krasnoselskii-Mann iterations. We prove that the solution of this dynamical system converges weakly to a fixed point of the involving mapping. Next, we focus our attention on a regularized Krasnoselskii-Mann type dynamical system. Besides proving existence and uniqueness of strong global solutions, we show that the generated trajectories converge strongly to a unique solution of a variational inequality over the fixed point set. Also, we provide a convergence rate analysis for the regularized dynamical system.
ISSN:1468-9367
1468-9375
DOI:10.1080/14689367.2023.2287432