S-metrik uzaylar üzerinde sabit-nokta teoremlerinin çeşitli türleri

Year 2018, Volume: 20 Issue: 2, 211 - 223, 01.12.2018

Nihal Taş

https://doi.org/10.25092/baunfbed.426665

Cited By: 7

Abstract

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.

Keywords

S-metrik uzay, değiştirilmiş Hardy-Rogers tipinde daralma, Khan tipinde daralma, sabit nokta, sabit çember

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

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. 

Keywords

S-metric space, modified Hardy-Rogers type contraction, Khan type contraction, fixed point, fixed circle

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