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Firm non-expansive mappings in weak metric spaces
- Source :
- Archiv der Mathematik, Archiv der Mathematik, 2022, 119, pp.389-400
- Publication Year :
- 2021
-
Abstract
- We introduce the notion of firm non-expansive mapping in weak metric spaces, extending previous work for Banach spaces and certain geodesic spaces. We prove that, for firm non-expansive mappings, the minimal displacement, the linear rate of escape, and the asymptotic step size are all equal. This generalises a theorem by Reich and Shafrir.<br />12 pages. The new Section 3 contains a characterisation of the firm non-expansive mappings of one-dimensional asymmetric normed spaces. The reference list includes new entries. This version has been accepted by Archiv der Mathematik
- Subjects :
- Mathematics Subject Classification (2010): 47H09, 51F99
non-expansive mapping
metric functional
Mathematics - Metric Geometry
firm non-expansive
General Mathematics
FOS: Mathematics
weak metric
47H09, 51F99
Metric Geometry (math.MG)
[MATH]Mathematics [math]
[MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG]
firmly non-expansive
Subjects
Details
- Language :
- English
- ISSN :
- 0003889X and 14208938
- Database :
- OpenAIRE
- Journal :
- Archiv der Mathematik, Archiv der Mathematik, 2022, 119, pp.389-400
- Accession number :
- edsair.doi.dedup.....48594f7a0e20d00851dc2f5edf3d0550