Hybrid Contractions on Branciari Type Distance Spaces

Kamaleldin Abodayeh,Erdal Karapınar,Ariana Pitea,Wasfi Shatanawi

doi:10.3390/math7100994

Abstract

In this manuscript, we consider some hybrid contractions that merge linear and nonlinear contractions in the abstract spaces induced by the Branciari distance and the Branciari b-distance. More precisely, we introduce the notion of a ( p , c ) -weight type ψ -contraction in the setting of Branciari distance spaces and the concept of a ( p , c ) -weight type contraction in Branciari b-distance spaces. We investigate the existence of a fixed point of such operators in Branciari type distance spaces and illustrate some examples to show that the presented results are genuine in the literature.

Highlights

The notion of metric spaces has many generalizations, in which each puts in the limelight the importance of the conditions that define them
(respectively, Branciari b-distance [2]) is obtained by replacing the triangle inequality axiom with the quadrilateral inequality axiom in the definition of a standard metric
Regarding the basic three axioms of the standard metric space, we notice that almost all generalization and extension presume the first of them

Summary

Introduction

The notion of metric spaces has many generalizations, in which each puts in the limelight the importance of the conditions that define them. Most of the generalizations of metric are obtained by relaxing one of its three axioms: self-distance, symmetry and the triangle inequality. There are several extensions of metric spaces, such as symmetric, quasi-metric, fuzzy metric, cone-metric, G-metric, b-metric and so on. In this manuscript, we prefer to investigate hybrid contractions in the abstract spaces induced by Branciari distance. (respectively, Branciari b-distance [2]) is obtained by replacing the triangle inequality axiom with the quadrilateral inequality (quadrilateral inequality multiplied by a constant s) axiom in the definition of a standard metric. Despite the apparent similarity between the definitions of the standard metric and Branciari distance (respectively, Branciari b-distance), the corresponding topologies are quite different

Objectives

Results

Conclusion