S-metrik uzaylarda ikili tipinde daralmalar yardımıyla yeni sabit-disk sonuçları

Yıl 2022, Cilt: 24 Sayı: 1, 408 - 416, 05.01.2022

Nihal Taş

https://doi.org/10.25092/baunfbed.995307

Öz

Banach daralma koşulunu sağlamayan ve bir tek sabit noktası ya da birden fazla sabit noktası olan fonksiyon örnekleri mevcuttur. Bu durumda, metrik sabit-nokta teorisi bazı teknikler kullanılarak kapsamlı olarak genelleştirilmektedir. Bu tekniklerden biri Jaggi tipinde daralma koşulu, Dass-Gupta tipinde daralma koşulu gibi kullanılan daralma koşulunun genelleştirilmesidir. Diğer bir teknik ise b-metrik uzay, S-metrik uzay gibi kullanılan metrik uzayın genelleştirilmesidir. Son teknik ise sabit çember, sabit disk gibi verilen bir fonksiyonun sabit nokta kümesinin geometrik özelliklerinin incelenmesidir. Bu amaç için, “sabit-çember problemi” metrik sabit-nokta teorisinin geometrik bir genellemesi olarak çeşitli tekniklerle çalışılmaktadır. Bu problem ayrıca “sabit-figür problemi” olarak da düşünülebilir. Bu son problemlere bazı çözümler hem metrik uzaylar üzerinde hem de genelleştirilmiş metrik uzaylar üzerinde farklı daralmalar kullanılarak elde edilmiştir. Bu makalenin ana amacı S-metrik uzaylar üzerinde bazı sabit-disk teoremleri ispatlamaktır. Bunun için, Bunun için bilinen bazı daralma koşullarını modifiye edeceğiz. Ayrıca elde edilen bu yeni teoremleri bazı gerçekleyici örnekler ile destekleyeceğiz.

Anahtar Kelimeler

Sabit disk, sabit çember, ikili tipinde daralma, S-metrik uzay, sabit çember problemi

New fixed-disc results via bilateral type contractions on S-metric spaces

Öz

There are some examples of self-mappings which does not satisfy the Banach contractive condition and have a unique fixed point or more than one fixed point. In this case, metric fixed-point theory has been extensively generalized using some techniques. One of these techniques is to generalize the used contractive conditions such as the Jaggi type contractive condition, the Dass-Gupta type contractive condition etc. Another technique is to generalize the used metric spaces such as a b-metric space, an S-metric space etc. The last technique is to investigate geometric properties of the fixed-point set of a given self-mapping such as fixed circle, fixed disc etc. For this purpose, “fixed-circle problem” has been studied with various techniques as a geometrical generalization of the metric fixed-point theory. This problem was also considered as “fixed-figure problem”. Some solutions to these recent problems were obtained using different contractions both a metric space and a generalized metric space. The main purpose of this paper is to prove some fixed-disc theorems on an S-metric space. To do this, we modify the known contractive conditions. Also, the obtained new theorems are supported by some illustrative examples.

Anahtar Kelimeler

Fixed disc, fixed circle, bilateral type contraction, S-metric space, fixed-circle problem

Kaynakça

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