Geraghty Contractions in Ordered Uniform Spaces

Year 2019, , 970 - 973, 25.12.2019

Vildan Öztürk

https://doi.org/10.19113/sdufenbed.569359

Cited By: 1

Abstract

Banach
contraction principle is  first and most
essential result in the fixed point theory. There are many generalisations of
this principle in the literature. One of them is Geraghty contraction. In this
work, Geraghty type contraction was defined via E-distance and common fixed
point theorems were proved for two mappings satisfying Geraghty type
contraction in ordered uniform spaces. Also, some results of these theorems were
obtained.

Keywords

Fixed point, E-distance function, Geraghty contraction, Uniform space

Sıralı Düzgün Uzaylarda Geraghty Büzülmeler

Abstract

Banach
büzülme prensibi, sabit nokta teorinin ilk ve en önemli sonucudur. Bu prensibin
literatürde pek çok genelleştirmesi vardır. Bunlardan biri de Geraghty
dönüşümüdür.  Bu çalışmada, sıralı düzgün
uzaylarda, E-uzaklık fonksiyonu yardımıyla, Geraghty tipli büzülme tanımlanmış
ve Geraghty tipli büzülmeyi sağlayan iki dönüşüm için ortak sabit nokta teoremleri
ispatlanmıştır. Ayrıca bu teoremlerin bazı sonuçları elde edilmiştir.

Keywords

Sabit nokta, E-uzaklık fonksiyonu, Geraghty büzülme, Düzgün uzay

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