Partial Metrics Viewed as w-Distances: Extending Some Powerful Fixed-Point Theorems

Involving w-distances and hybrid contractions that combine conditions of the Ćirić type and Samet et al. type, we obtain some general fixed-point results for quasi-metric spaces from which powerful and significant fixed-point theorems on partial metric spaces are deduced as special cases. We present...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 12; no. 24; p. 3991
Main Authors: Romaguera, Salvador, Tirado, Pedro
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.12.2024
Subjects:
Analysis
fixed point
Fixed point theory
Fixed points (mathematics)
hybrid contraction
Metric space
Metric spaces
partial metric
quasi-metric
Recursive functions
strong w-distance
Theorems
weighted
Spain
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary:Involving w-distances and hybrid contractions that combine conditions of the Ćirić type and Samet et al. type, we obtain some general fixed-point results for quasi-metric spaces from which powerful and significant fixed-point theorems on partial metric spaces are deduced as special cases. We present examples showing that our results are real generalizations of those corresponding to the partial metric case and we give an application to the study of recursive equations where the usual Baire partial metric on a domain of words is replaced with a suitable w-distance. Our approach is inspired on the nice fact, stated by Matthews, that every partial metric induces a weighted quasi-metric. Then, we define the notion of a strong w-distance and deduce that every partial metric is a symmetric strong w-distance for its induced weighted quasi-metric space.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math12243991