Partial Metrics Viewed as <i>w</i>-Distances: Extending Some Powerful Fixed-Point Theorems
Involving <i>w</i>-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 specia...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/12/24/3991 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850085142420258816 |
|---|---|
| author | Salvador Romaguera Pedro Tirado |
| author_facet | Salvador Romaguera Pedro Tirado |
| author_sort | Salvador Romaguera |
| collection | DOAJ |
| description | Involving <i>w</i>-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 <i>w</i>-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 <i>w</i>-distance and deduce that every partial metric is a symmetric strong <i>w</i>-distance for its induced weighted quasi-metric space. |
| format | Article |
| id | doaj-art-2f6528599e904dbc9f93408690fe436e |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-2f6528599e904dbc9f93408690fe436e2025-08-20T02:43:49ZengMDPI AGMathematics2227-73902024-12-011224399110.3390/math12243991Partial Metrics Viewed as <i>w</i>-Distances: Extending Some Powerful Fixed-Point TheoremsSalvador Romaguera0Pedro Tirado1Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, SpainInstituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, SpainInvolving <i>w</i>-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 <i>w</i>-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 <i>w</i>-distance and deduce that every partial metric is a symmetric strong <i>w</i>-distance for its induced weighted quasi-metric space.https://www.mdpi.com/2227-7390/12/24/3991quasi-metricweightedpartial metricstrong w-distancehybrid contractionfixed point |
| spellingShingle | Salvador Romaguera Pedro Tirado Partial Metrics Viewed as <i>w</i>-Distances: Extending Some Powerful Fixed-Point Theorems Mathematics quasi-metric weighted partial metric strong w-distance hybrid contraction fixed point |
| title | Partial Metrics Viewed as <i>w</i>-Distances: Extending Some Powerful Fixed-Point Theorems |
| title_full | Partial Metrics Viewed as <i>w</i>-Distances: Extending Some Powerful Fixed-Point Theorems |
| title_fullStr | Partial Metrics Viewed as <i>w</i>-Distances: Extending Some Powerful Fixed-Point Theorems |
| title_full_unstemmed | Partial Metrics Viewed as <i>w</i>-Distances: Extending Some Powerful Fixed-Point Theorems |
| title_short | Partial Metrics Viewed as <i>w</i>-Distances: Extending Some Powerful Fixed-Point Theorems |
| title_sort | partial metrics viewed as i w i distances extending some powerful fixed point theorems |
| topic | quasi-metric weighted partial metric strong w-distance hybrid contraction fixed point |
| url | https://www.mdpi.com/2227-7390/12/24/3991 |
| work_keys_str_mv | AT salvadorromaguera partialmetricsviewedasiwidistancesextendingsomepowerfulfixedpointtheorems AT pedrotirado partialmetricsviewedasiwidistancesextendingsomepowerfulfixedpointtheorems |