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Journals / Hacettepe Journal of Mathematics and Statistics / 2023 / Cilt: 52 Sayı: 6 - Special Issue: Nonlinear Evolution Problems with Applications

Algorithm analysis of solving fixed point of nonexpansive mappings based on runge-kutta method

Xiangyao Lİ
Li-jun ZHU
Mihai POSTOLACHE
Pages
1567–1577
Publication Date
2023-11-03
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We show that the second algorithm is bounded perturbations resilient, and it is strongly convergent.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In order to solve the fixed point of nonexpansive mappings, we propose two iterative algorithms based on runge-kutta method.
📊
Key Findings & Data:The first algorithm is focused on solving the fixed point problem of a single nonexpansive mapping, and weak convergence has been proved. we suggest the second algorithm by dynamic string-averaging rule.
💡
Conclusion & Impact:We show that the second algorithm is bounded perturbations resilient, and it is strongly convergent.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:nonexpansive mapping · common fixed point · runge-kutta method

Abstract

In order to solve the fixed point of nonexpansive mappings, we propose two iterative algorithms based on runge-kutta method. The first algorithm is focused on solving the fixed point problem of a single nonexpansive mapping, and weak convergence has been proved. we suggest the second algorithm by dynamic string-averaging rule. It can be used to find a common fixed point of a family of finite nonexpansive mappings. We show that the second algorithm is bounded perturbations resilient, and it is strongly convergent.

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Cite This Article

Lİ, X., ZHU, L., POSTOLACHE, M. (2023). Algorithm analysis of solving fixed point of nonexpansive mappings based on runge-kutta method. Hacettepe Journal of Mathematics and Statistics, Cilt: 52 Sayı: 6 - Special Issue: Nonlinear Evolution Problems with Applications, 1567–1577. https://ajindex.com/articles/971786

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