Published October 8, 2018
| Version v1
Journal article
Open
On Completeness in Metric Spaces and Fixed Point Theorems
- 1. Polytechnic University of Valencia
- 2. University of the Balearic Islands
Description
Complete ultrametric spaces constitute a particular class of the so called, recently, G-complete metric spaces. In this paper we characterize a more general class called weak G-complete metric spaces, by means of nested sequences of closed sets. Then, we also state a general fixed point theorem for a self-mapping of a weak G-complete metric space. As a corollary, every asymptotically regular self-mapping of a weak G-Complete metric space has a fixed point.
Notes
This is a preprint of the publication available from https://link.springer.com/article/10.1007/s00025-018-0896-4. This work is also supported by project PGC2018-095709-B-C21 (MCIU/AEI/FEDER, UE), and PROCOE/4/2017 (Govern Balear, 50% P.O. FEDER 2014-2020 Illes Balears).
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