On quasihyperbolic geodesics in banach spaces

TY - JOUR

T1 - On quasihyperbolic geodesics in banach spaces

AU - Rasila, Antti

AU - Talponen, Jarno

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Banach space

KW - C smoothness

KW - Convex domain

KW - Quasihyperbolic geodesic

KW - Quasihyperbolic metric

KW - Radon-Nikodym property

KW - Reflexive

KW - Renormings

KW - Uniform convexity

UR - http://www.scopus.com/inward/record.url?scp=84893844005&partnerID=8YFLogxK

U2 - 10.5186/aasfm.2014.3924

DO - 10.5186/aasfm.2014.3924

M3 - 文章

AN - SCOPUS:84893844005

SN - 1239-629X

VL - 39

SP - 163

EP - 173

JO - Annales Academiae Scientiarum Fennicae Mathematica

JF - Annales Academiae Scientiarum Fennicae Mathematica

IS - 1

ER -