Abstract
In this paper we consider a kind of Geraghty contractions by using mw-distances in the setting of complete quasi-metric spaces. We provide fixed point theorems for this type of mappings and illustrate with some examples the results obtained.
Highlights
Introduction and PreliminariesIn 1973, Geraghty proved the following fixed point theorem which generalizes the classical Banach fixed point theorem.Theorem 1 ([1])
The mapping T : X → X has a unique fixed point provided that there exists β ∈ B such that d ( T κ, Tν) ≤ β(d (κ, ν))d (κ, ν), for all κ, ν ∈ X
Cho et al [3] defined the notion of α-Geraghty contraction in the context of a metric space, as follows: A maping T is called a α-Geraghty contraction if α(κ, ν)d ( T κ, Tν) ≤ β(d (κ, ν)) max{d (κ, ν), d (ν, Tν), d (κ, T κ)}, for all κ,ν ∈ X, where α : X × X → [0, ∞) is a function with the property
Summary
Introduction and PreliminariesIn 1973, Geraghty proved the following fixed point theorem which generalizes the classical Banach fixed point theorem.Theorem 1 ([1]).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
