Bibliographic Details
| Title: |
On Protected Quasi-Metrics. |
| Authors: |
Romaguera, Salvador1 (AUTHOR) sromague@mat.upv.es |
| Superior Title: |
Axioms (2075-1680). Mar2024, Vol. 13 Issue 3, p158. 16p. |
| Subject Terms: |
*QUASI-metric spaces, *DIFFERENCE equations |
| 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] |
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