The Meir–Keeler Fixed Point Theorem for Quasi-Metric Spaces and Some Consequences

We obtain quasi-metric versions of the famous Meir–Keeler fixed point theorem from which we deduce quasi-metric generalizations of Boyd–Wong’s fixed point theorem. In fact, one of these generalizations provides a solution for a question recently raised in the paper “On the fixed point theory in bico...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 11; no. 6; p. 741
Main Authors Romaguera, Salvador, Tirado, Pedro
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.06.2019
Subjects
Boyd–Wong
Difference equations
fixed point
Fixed points (mathematics)
Mathematical analysis
Meir–Keeler
Metric space
quasi-metric space
Theorems
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Summary:We obtain quasi-metric versions of the famous Meir–Keeler fixed point theorem from which we deduce quasi-metric generalizations of Boyd–Wong’s fixed point theorem. In fact, one of these generalizations provides a solution for a question recently raised in the paper “On the fixed point theory in bicomplete quasi-metric spaces”, J. Nonlinear Sci. Appl. 2016, 9, 5245–5251. We also give an application to the study of existence of solution for a type of recurrence equations associated to certain nonlinear difference equations.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym11060741