Abstract
We study properties of quasihyperbolic geodesics on Banach spaces. For example, we show that in a strictly convex Banach space with the Radon-Nikodym property, the quasihyperbolic geodesics are unique. We also give an example of a convex domain ω in a Banach space such that there is no geodesic between any given pair of points x, y ∈ ω. In addition, we prove that if X is a uniformly convex Banach space and its modulus of convexity is of a power type, then every geodesic of the quasihyperbolic metric, defined on a proper subdomain of X, is smooth.
Original language | English |
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Pages (from-to) | 163-173 |
Number of pages | 11 |
Journal | Annales Academiae Scientiarum Fennicae Mathematica |
Volume | 39 |
Issue number | 1 |
DOIs | |
State | Published - 2014 |
Externally published | Yes |
Keywords
- Banach space
- C smoothness
- Convex domain
- Quasihyperbolic geodesic
- Quasihyperbolic metric
- Radon-Nikodym property
- Reflexive
- Renormings
- Uniform convexity