Path--Averaged Contractions: A New Generalization of the Banach Contraction Principle
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914071445504000 |
|---|---|
| author | Fabiano, Nicola |
| author_facet | Fabiano, Nicola |
| contents | We introduce a novel class of self-mappings on metric spaces, called \textbf{PA-contractions} (Path-Averaged Contractions), defined by an averaging condition over iterated distances. We prove that every continuous PA-contraction on a complete metric space has a unique fixed point, and the Picard iterates converge to it. This condition strictly generalizes the classical Banach contraction principle. We provide examples showing that PA-contractions are independent of F-contractions, Kannan, Chatterjea, and Ćirić contractions. A comparison table highlights the distinctions. The PA-condition captures long-term contractive behavior even when pointwise contraction fails. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01496 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Path--Averaged Contractions: A New Generalization of the Banach Contraction Principle Fabiano, Nicola Functional Analysis 47H10 47H10, 54E50 We introduce a novel class of self-mappings on metric spaces, called \textbf{PA-contractions} (Path-Averaged Contractions), defined by an averaging condition over iterated distances. We prove that every continuous PA-contraction on a complete metric space has a unique fixed point, and the Picard iterates converge to it. This condition strictly generalizes the classical Banach contraction principle. We provide examples showing that PA-contractions are independent of F-contractions, Kannan, Chatterjea, and Ćirić contractions. A comparison table highlights the distinctions. The PA-condition captures long-term contractive behavior even when pointwise contraction fails. |
| title | Path--Averaged Contractions: A New Generalization of the Banach Contraction Principle |
| topic | Functional Analysis 47H10 47H10, 54E50 |
| url | https://arxiv.org/abs/2510.01496 |