Monotone Picard Maps in Relational Metric Spaces

The 2008 fixed point result on rs-relational metric spaces due to Jachymski is equivalent with the classical 1922 Banach Contraction Principle. This is also valid for the 1961 statement in metric spaces due to Edelstein, or the 2005 fixed point result in quasi-ordered metric spaces obtained by Nieto and Rodriguez-Lopez.

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Journal
Mathematics
Published
2025-11-03
DOI
https://doi.org/10.3390/math13213518
Primary Topic
Fixed Point Theorems Analysis
Type
article
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Monotone Picard Maps in Relational Metric Spaces

Mihai Turinici
Mathematics
Fixed Point Theorems Analysis
article

Monotone Picard Maps in Relational Metric Spaces

Mihai Turinici
article en

Abstract

The 2008 fixed point result on rs-relational metric spaces due to Jachymski is equivalent with the classical 1922 Banach Contraction Principle. This is also valid for the 1961 statement in metric spaces due to Edelstein, or the 2005 fixed point result in quasi-ordered metric spaces obtained by Nieto and Rodriguez-Lopez.

MathematicsVol. 13(21)
Alexandru Ioan Cuza University (RO)
Openalex Percentile: Top 62%
Fixed Point Theorems Analysis
DOIOpen Access PDFOpenAlex
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Monotone Picard Maps in Relational Metric Spaces — Mihai Turinici · Mathematics (2025) | TGRS Research Map | TGRS