Displaying similar documents to “Invariant metrics on convex cones”

Iterates of maps which are non-expansive in Hilbert's projective metric

Jeremy Gunawardena, Cormac Walsh (2003)

Kybernetika

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The cycle time of an operator on R n gives information about the long term behaviour of its iterates. We generalise this notion to operators on symmetric cones. We show that these cones, endowed with either Hilbert’s projective metric or Thompson’s metric, satisfy Busemann’s definition of a space of non- positive curvature. We then deduce that, on a strictly convex symmetric cone, the cycle time exists for all maps which are non-expansive in both these metrics. We also review an analogue...

The Demyanov metric and some other metrics in the family of convex sets

Tadeusz Rzeżuchowski (2012)

Open Mathematics

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We describe some known metrics in the family of convex sets which are stronger than the Hausdorff metric and propose a new one. These stronger metrics preserve in some sense the facial structure of convex sets under small changes of sets.

On some aspects of Jensen-Menger convexity.

Joanna Ger, Roman Ger (1992)

Stochastica

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The paper contains various results concerning the so-called homogeneity sets for convex functions defined on convex subsets of some special metric spaces named G-space (cf. H. Busemann [1]). A closed graph theorem for such type mappings is also presented.