Geraghty Contractions in Ordered Uniform Spaces

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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