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Journals / Sigma Mühendislik ve Fen Bilimleri Dergisi / 2019 / Volume: 37 Issue: 3

SOME FIXED POINT RESULTS FOR CONTINUOUS FUNCTIONS ON AN ARBITRARY INTERVALS

Kadri Dogan Dogan(Artvin Coruh University, Department of Computer Engineering)
Faik Gursoy(Department of Mathematics, Adiyaman University)0000-0002-7118-9088
Vatan Karakaya(Yildiz Technical University, Dept. of Mathematical Engineering)0000-0003-4637-3139
Pages
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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.
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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, Volume: 37 Issue: 3. https://ajindex.com/articles/1344929

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