b-Metrik Uzaylarda φ-Sabit Nokta Teoremleri ve Uygulamaları

Bu çalışmanın amacı, b-metrik uzaylarda bazı yeni büzülmelerin φ-sabit noktalarının varlığını ve tekliğini göstermektir. Öncelikle, bu çalışmada, b-metrik uzaylarda (?,?,?,?)? ve (?,?,?,?)? –zayıf büzülme isimli iki tanım verilmiştir. Sonra, b-metrik uzaylarda bu tanımlar için ?-sabit nokta teoremleri ispatlanmıştır. Uygulama olarak, kısmi metrik uzayların genelleştirmesi olan tam kısmi b-metrik uzaylarda bazı sabit nokta sonuçları verilmiştir. Bu çalışmada elde edilen teoremler, literatürde bilinen φ-sabit nokta sonuçlarından daha genel ve geniş olduğu gibi, literatürde var olan bazı sabit nokta sonuçlarından da daha geneldir.

Some φ-Fixed Point Results in b−Metric Spaces and Applications

The purpose of this study is to introduce the existence and uniqueness of φ-fixed point for some new contractions in complete b-metric spaces. Firstly, in this paper, we presented new definitions called (?,?,?,?)? and (?,?,?,?)? -weak contractions in complete b-metric spaces as a generalization of metric spaces. Later, we proved ?-fixed point theorems for (?,?,?,?)? and (?,?,?,?)?-weak contractions in complete b-metric spaces. As applications, we derived some fixed point results in complete partial b-metric spaces as a generalization of partial metric spaces. The presented theorems extend and generalize some ?-fixed point results which are known in the literature. Also, some results in this paper generalizes many existing some fixed point results in the literature.

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