Common Fixed Point under Nonlinear Contractions on Quasi Metric Spaces

Wasfi Shatanawi,Kamaleldin Abodayeh

doi:10.3390/math7050453

Wasfi Shatanawi, Kamaleldin Abodayeh

Open Access

https://doi.org/10.3390/math7050453

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Abstract

We introduce in this article the notion of ( ψ , ϕ ) - quasi contraction for a pair of functions on a quasi-metric space. We also investigate the existence and uniqueness of the fixed point for a couple functions under that contraction.

Highlights

Introduction and PreliminaryFixed point has been considered by many researchers since it was established by Banach [1]in 1992
The generalizations of the theory were considered by many researchers on various metric spaces
Quasi-metric space was one of the interesting examples that were considered since it was introduced by Wilson [8] in 1931

Summary

Introduction and Preliminary

Fixed point has been considered by many researchers since it was established by Banach [1]. The generalizations of the theory were considered by many researchers on various metric spaces (see, for example, [2,3,4,5,6,7]). Quasi-metric space was one of the interesting examples that were considered since it was introduced by Wilson [8] in 1931. [8] Let χ be a non-empty set and ρ : χ × χ → [0, ∞) be a given function that satisfies the following conditions:. Consider the set χ = [0, 1] and define the function ρ : χ × χ → [0, ∞) such that We need to verify the two conditions of Definition 1.

Case III

By taking