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- Title
ON PROPERTIES OF CONTRACTIONS AND NONEXPANSIVE MAPPINGS ON SPHERICAL CAPS IN HILBERT SPACES.
- Authors
BOLIBOK, KRZYSZTOF; SZCZEPANIK, MARIUSZ
- Abstract
Let H be an at least two-dimensional real Hilbert space with the unit sphere SH. For α ∈[-1; 1] and n ∈SH we define an (α; n)-spherical cap by Sα;n = {x ∈SH : [x,n]≤ α}. We show that the distance between the set of contractions T : Sα;n → Sα;n and the identity mapping is positive iα α < 0: We also study the fixed point property and the minimal displacement problem in this setting for nonexpansive mappings.
- Subjects
NONEXPANSIVE mappings; HILBERT space; SET theory; FIXED point theory; MATHEMATICAL analysis
- Publication
Fixed Point Theory, 2017, Vol 18, Issue 2, p471
- ISSN
1583-5022
- Publication type
Article
- DOI
10.24193/fpt-ro.2017.2.37