Back to Search
Start Over
On Protected Quasi-Metrics.
- Source :
-
Axioms (2075-1680) . Mar2024, Vol. 13 Issue 3, p158. 16p. - Publication Year :
- 2024
-
Abstract
- In this paper, we introduce and examine the notion of a protected quasi-metric. In particular, we give some of its properties and present several examples of distinguished topological spaces that admit a compatible protected quasi-metric, such as the Alexandroff spaces, the Sorgenfrey line, the Michael line, and the Khalimsky line, among others. Our motivation is due, in part, to the fact that a successful improvement of the classical Banach fixed-point theorem obtained by Suzuki does not admit a natural and full quasi-metric extension, as we have noted in a recent article. Thus, and with the help of this new structure, we obtained a fixed-point theorem in the framework of Smyth-complete quasi-metric spaces that generalizes Suzuki's theorem. Combining right completeness with partial ordering properties, we also obtained a variant of Suzuki's theorem, which was applied to discuss types of difference equations and recurrence equations. [ABSTRACT FROM AUTHOR]
- Subjects :
- *QUASI-metric spaces
*DIFFERENCE equations
Subjects
Details
- Language :
- English
- ISSN :
- 20751680
- Volume :
- 13
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Axioms (2075-1680)
- Publication Type :
- Academic Journal
- Accession number :
- 176270507
- Full Text :
- https://doi.org/10.3390/axioms13030158