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Journals / Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2018 / Cilt: 20 Sayı: 2

Various types of fixed-point theorems on S-metric spaces

S-metrik uzaylar üzerinde sabit-nokta teoremlerinin çeşitli türleri

Nihal Taş
Pages
211–223
Publication Date
2018-12-01
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AI Summary & Key Takeaways

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

As an application, a new fixed-circle result is presented using modified C-Khan type contraction on S-metric spaces.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Recently, some generalized metric spaces have been studied to obtain new fixed-point theorems.
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Key Findings & Data:Also, to illustrate obtained theoretical results, some examples are given using an S-metric which is not generated by any metric.
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Conclusion & Impact:As an application, a new fixed-circle result is presented using modified C-Khan type contraction on S-metric spaces.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:S-metrik uzay · değiştirilmiş Hardy-Rogers tipinde daralma · Khan tipinde daralma

Abstract

Recently, some generalized metric spaces have been studied to obtain new fixed-point theorems. For example, the notion of S-metric space was introduced for this purpose. In this study, some fixed-point results are proved using different contractive conditions on S-metric spaces. Various techniques such as Hard-Rogers type contraction, Khan type contraction, Meir-Keeler-Khan type contraction are used in our theorems to be proved. These fixed-point results extend some known fixed-point theorems on S-metric spaces. Also, to illustrate obtained theoretical results, some examples are given using an S-metric which is not generated by any metric. As an application, a new fixed-circle result is presented using modified C-Khan type contraction on S-metric spaces.

Özet

Son zamanlarda yeni sabit nokta teoremleri elde etmek için bazı genelleştirilmiş metrik uzaylar çalışılmaktadır. Örneğin, S-metrik uzay kavramı bu amaç için tanıtılmıştır. Bu çalışmada, S-metrik uzaylar üzerinde farklı daralma koşulları kullanılarak bazı sabit nokta sonuçları ispatlanmıştır. İspatlanan teoremlerde Hardy-Rogers tipinde daralma, Khan tipinde daralma, Meir-Keeler-Khan tipinde daralma gibi çeşitli teknikler kullanılmıştır. Bu sabit nokta sonuçları S-metrik uzaylar üzerindeki bazı bilinen sabit nokta sonuçlarını genellemektedir. Ayrıca, herhangi bir metrik tarafından üretilemeyen S-metrik örnekleri kullanılarak elde edilen teorik sonuçları gerçekleyecek bazı örnekler verilmiştir. S-metrik uzaylar üzerinde bir uygulama olarak değiştirilmiş C-Khan tipinde daralma kavramı kullanılarak yeni bir sabit çember sonucu verilmiştir.

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Cite This Article

Taş, N. (2018). Various types of fixed-point theorems on S-metric spaces. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 20 Sayı: 2, 211–223. https://doi.org/10.25092/baunfbed.426665

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