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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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
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Abstract 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.
AbstractList 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.
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.
Author Tirado, Pedro
Romaguera, Salvador
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crossref_primary_10_1007_s40819_021_01129_9
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Snippet 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...
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...
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SubjectTerms Boyd–Wong
Difference equations
fixed point
Fixed points (mathematics)
Mathematical analysis
Meir–Keeler
Metric space
quasi-metric space
Theorems
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Title The Meir–Keeler Fixed Point Theorem for Quasi-Metric Spaces and Some Consequences
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