Partial Metrics Viewed as w-Distances: Extending Some Powerful Fixed-Point Theorems
[EN] Involving w-distances and hybrid contractions that combine conditions of the & Cacute;iri & cacute; 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 ar...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/220041 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/220041 |
| Access Level: | acceso abierto |
| Palabra clave: | Quasi-metric Weighted Partial metric Strong w-distance Hybrid contraction Fixed point |
| Sumario: | [EN] Involving w-distances and hybrid contractions that combine conditions of the & Cacute;iri & cacute; 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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