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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2020 / Volume: 69 Issue: 2

On the geometry of fixed points of self-mappings on S-metric spaces

Nihal Özgür(BALIKESIR UNIVERSITY)0000-0002-8152-1830
Nihal Taş(BALIKESIR UNIVERSITY)0000-0002-4535-4019
Pages
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Publication Date
2020-12-31
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AI Summary & Key Takeaways

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

In Section 4, we summarize our study and recommend some future works.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we focus on some geometric properties related to the set Fix(T), the set of all fixed points of a mapping T:X→X, on an S-metric space (X,S).
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Key Findings & Data:In Section 2, we prove some fixed circle and fixed disc results using different approaches.
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Conclusion & Impact:In Section 4, we summarize our study and recommend some future works.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:$S$-metric space · fixed circle · $S$-Pata type $x_{0}$-mapping

Abstract

In this paper, we focus on some geometric properties related to the set Fix(T), the set of all fixed points of a mapping T:X→X, on an S-metric space (X,S). For this purpose, we present the notions of an S-Pata type x₀-mapping and an S-Pata Zamfirescu type x₀-mapping. Using these notions, we propose new solutions to the fixed circle (resp. fixed disc) problem. Also, we give some illustrative examples of our main results. In this paper, we give new solutions to the fixed circle (resp. fixed disc) problem on S-metric spaces. In Section 2, we prove some fixed circle and fixed disc results using different approaches. In Section 3, we give some illustrative examples of our obtained results and deduce some important remarks. In Section 4, we summarize our study and recommend some future works.

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Cite This Article

Özgür, N., Taş, N. (2020). On the geometry of fixed points of self-mappings on S-metric spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 69 Issue: 2. https://doi.org/10.31801/cfsuasmas.616325

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