Common Fixed Point Results for w-α-Distance

Year 2024, , 7 - 11, 01.07.2024

Gülcan Atıci Turan , Fatma Polat

https://doi.org/10.18586/msufbd.1367657

Abstract

In this study, we examined some fixed point theorems in non-full metric spaces. We define the notions of α-lower semi-continuous , w-α-distance, w_0-α– distance, w-α-rational contraction and generalized w-α-rational contraction mapping. We also give related theorem and example. Then, we prove Banach’s fixed-point theorem thanks to the concept w-α- distance in metric spaces equipped with an abritrary binary relation. Also, w-α- rational contraction mapping and generalized w-α-rational contraction mapping are defined and by using these definitions, the theorem related fixed point is expressed and proved.

Keywords

Binary Relation, Fixed Point, α-Complete Metric Space, w-Distance.

Common Fixed Point Results for w-α-distance

Abstract

Bu çalışmada, tam olmayan metrik uzaylarda bazı sabit nokta teoremlerini inceledik. Alt yarı-sürekli, --uzaklık, --uzaklık, --rasyonel daralma ve genelleştirilmiş --rasyonel daralma eşlemesi kavramlarını tanımladık. Ayrıca ilgili teoremi ve örneği veriyoruz. Daha sonra, Banach'ın sabit nokta teoremini metrik uzaylarda - - uzaklık kavramı sayesinde ispatlıyoruz. Ayrıca - - rasyonel daralma haritalaması ve genelleştirilmiş - - rasyonel daralma haritalaması tanımlanmış ve bu tanımlar kullanılarak sabit nokta ile ilgili teorem ifade edilmiş ve ispatlanmıştır.

Keywords

İkili bağıntı, Sabit nokta, α-tam metrik uzay, w-mesafe

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