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- Title
A POROSITY RESULT REGARDING FIXED POINTS FOR A CLASS OF NONEXPANSIVE MAPPINGS.
- Authors
REICH, SIMEON; ZASLAVSKI, ALEXANDER J.
- Abstract
In one of our recent papers, we considered a complete metric space of nonexpansive mappings taking a bounded and closed subset of a complete hyperbolic space into the space so that the boundary of this subset is mapped back into the subset itself. Using the Baire category approach, we proved that most of these mappings possess a unique fixed point which attracts all their iterates. In the present paper, we improve upon this result by showing that the complement of the set of mappings which have a fixed point is not only of the first Baire category, but also is s-porous.
- Subjects
FIXED point theory; NONEXPANSIVE mappings; METRIC spaces; HYPERBOLIC spaces; ITERATIVE methods (Mathematics); SET theory
- Publication
Applied Set-Valued Analysis & Optimization, 2022, Vol 4, Issue 3, p375
- ISSN
2562-7775
- Publication type
Article
- DOI
10.23952/asvao.4.2022.3.10