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Journals / Erciyes Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2019 / Cilt: 35 - Sayı: 3

Obtaining New Fixed Point Theorems By Using Generalized Banach-Contraction Principle

Genelleştirilmiş Banach-Büzülme Prensibi Kullanılarak Yeni Sabit Nokta Teoremlerinin Elde Edilmesi

Yunus ATALAN
Vatan KARAKAYA
Pages
34–45
Publication Date
2022-11-03
DOI
—
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⚡ TL;DR(Too Long; Didn't Read)

Inaddition, it was shown that the new iterative algorithm has a better convergencespeed when compared the other Jungck-type iterative algorithms in the currentliterature, and to support this result, numerical examples were given.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, a new three step iterative algorithm was introduced withthe help of Jungck-contraction principle which is one of the remerkablegeneralizations of Banach-contraction principle.
📊
Key Findings & Data:Also, the convergence and stabilityresults were obtained for the pair of nonself mappings which satisfy a certaincontractive condition by using this iterative algorithm in any Banach space.
💡
Conclusion & Impact:Inaddition, it was shown that the new iterative algorithm has a better convergencespeed when compared the other Jungck-type iterative algorithms in the currentliterature, and to support this result, numerical examples were given.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this study, a new three step iterative algorithm was introduced withthe help of Jungck-contraction principle which is one of the remerkablegeneralizations of Banach-contraction principle. Also, the convergence and stabilityresults were obtained for the pair of nonself mappings which satisfy a certaincontractive condition by using this iterative algorithm in any Banach space. Inaddition, it was shown that the new iterative algorithm has a better convergencespeed when compared the other Jungck-type iterative algorithms in the currentliterature, and to support this result, numerical examples were given.

Özet

Bu çalışmada, Banach-büzülme prensibinin dikkate değer genellemelerinden biri olan Jungck-büzülme prensibi yardımıyla yeni üç adımlı iterasyon algoritması tanımlanmıştır. Ayrıca bu iterasyon algoritması kullanılarak, kendi üzerine olmayan ve belirli bir büzülme şartını sağlayan dönüşüm çifti için herhangi bir Banach uzayında yakınsaklık ve kararlılık sonuçları elde edilmiştir. Ek olarak, tanımlanan yeni algoritmanın literatürde bulunan diğer Jungck-tipindeki algoritmalarla kıyaslandığında yakınsama anlamında daha hızlı olduğu gösterilmiş ve bu sonucu destekleyen nümerik örnekler verilmiştir.

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Cite This Article

ATALAN, Y., KARAKAYA, V. (2022). Obtaining New Fixed Point Theorems By Using Generalized Banach-Contraction Principle. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 35 - Sayı: 3, 34–45. https://ajindex.com/articles/650136

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