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Journals / Sigma Mühendislik ve Fen Bilimleri Dergisi / 2019 / Cilt: 37 - Sayı: 3

SOME FIXED POINT RESULTS FOR CONTINUOUS FUNCTIONS ON AN ARBITRARY INTERVALS

Kadri Dogan DOGAN
Faik GURSOY
Vatan KARAKAYA
Pages
755–767
Publication Date
2020-09-01
DOI
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AI Summary & Key Takeaways

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

Finally, some numerical examples for comparing the rate of convergence of those methods are also given.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we first give a necessary and sufficient condition for convergence of Picard-S iteration process to a fixed point of continuous functions on an arbitrary interval and prove equivalence of Picard-S and P iterative processes.
📊
Key Findings & Data:We also compare the rate of convergence between Picard-S and some others iteration processes in the literature.
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Conclusion & Impact:Finally, some numerical examples for comparing the rate of convergence of those methods are also given.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Rate of convergence · Picard-S iteration process · continuous function

Abstract

In this paper, we first give a necessary and sufficient condition for convergence of Picard-S iteration process to a fixed point of continuous functions on an arbitrary interval and prove equivalence of Picard-S and P iterative processes. We also compare the rate of convergence between Picard-S and some others iteration processes in the literature. Finally, some numerical examples for comparing the rate of convergence of those methods are also given.

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Cite This Article

DOGAN, K. D., GURSOY, F., KARAKAYA, V. (2020). SOME FIXED POINT RESULTS FOR CONTINUOUS FUNCTIONS ON AN ARBITRARY INTERVALS. Sigma Mühendislik ve Fen Bilimleri Dergisi, Cilt: 37 - Sayı: 3, 755–767. https://ajindex.com/articles/419147

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