Annales Academię Scientiarum Fennicę
Mathematica
Volumen 37, 2012, 215-228
Aalto University, Institute of Mathematics
P.O. Box 11100, FI-00076 Aalto, Finland; antti.rasila 'at' iki.fi
Aalto University, Institute of Mathematics
P.O. Box 11100, FI-00076 Aalto, Finland; talponen 'at' cc.hut.fi
Abstract. We study the convexity and starlikeness of metric balls on Banach spaces when the metric is the quasihyperbolic metric or the distance ratio metric. In particular, problems related to these metrics on convex domains, and on punctured Banach spaces, are considered.
2010 Mathematics Subject Classification: Primary 30C65; Secondary 46T05.
Key words: Quasihyperbolic ball, quasihyperbolic geodesic, distance ratio metric.
Reference to this article: A. Rasila and J. Talponen: Convexity properties of quasihyperbolic balls on Banach spaces. Ann. Acad. Sci. Fenn. Math. 37 (2012), 215-228.
doi:10.5186/aasfm.2012.3719
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