A few properties of the Kobayashi distance and their applications

Jarosław Kapeluszny, Tadeusz Kuczumow

DOI: http://dx.doi.org/10.12775/TMNA.2000.013

Abstract


Let $N$ be a norming set in a Banach space $X$. In this paper we
prove the lower semicontinuity with respect to the topology
$\sigma( X,N)$ of the Kobayashi distance in a
bounded, relatively compact in $\sigma ( X,N) $, convex and open
subset of a Banach space. We apply this result to the Denjoy-Wolff
type theorem.

Keywords


The Denjoy-Wolff theorem; fixed-point-free mappings; holomorphic mappings; iterations of condensing mappings; the Kobayashi distance; Kuratowski's measure of noncompactness; nonexpansive mappings

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