### A few properties of the Kobayashi distance and their applications

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.

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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