Fixed points of α-admissible Meir-Keeler contraction mappings on quasi-metric spaces

Hamed H Alsulami,İnci M Erhan,Selma Gülyaz

doi:10.1186/s13660-015-0604-9

Abstract

We introduce α-admissible Meir-Keller and generalized α-admissible Meir-Keller contractions on quasi-metric spaces and discuss the existence of fixed points of such contractions. We apply our results to G-metric spaces and express some fixed point theorems in G-metric spaces as consequences of the results in quasi-metric spaces.

Highlights

Introduction and preliminariesOne of the generalizations of the metric spaces are the so-called quasi-metric spaces in which the commutativity condition does not hold in general
We investigate the existence of fixed points of Meir-Keeler type contractions defined on quasi-metric spaces and apply our results to G-metric spaces
We recall the definition of a quasi-metric and quasi-metric space and some topological concepts on these spaces

Summary

Introduction

Introduction and preliminariesOne of the generalizations of the metric spaces are the so-called quasi-metric spaces in which the commutativity condition does not hold in general. We investigate the existence of fixed points of Meir-Keeler type contractions defined on quasi-metric spaces and apply our results to G-metric spaces. 2 Main results Our first result is a fixed point theorem for generalized α-Meir-Keeler contractions of type (I) on quasi-metric spaces.

Results

Conclusion