Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2014-07-02
Kuratowski's Measure of Noncompactness with Respect to Thompson's MetricGerd Herzog and Peer Christian Kunstmann (1) Karlsruher Institut für Technologie (KIT), Germany
(2) Karlsruher Institut für Technologie (KIT), Germany
It is known that the interior of a normal cone $K$ in a Banach space is a complete metric space with respect to Thompson's metric $d$. We prove that Kuratowski's measure of noncompactness $\tau$ in $(K°; d)$ has the Mazur-Darbo property and that, as a consequence, an analog of Darbo-Sadovskii's xed point theorem is valid in $(K°; d)$. We show that the properties of $\tau$ partly differ to the classical case. Among others $\tau$ is nicely compatible with the multiplication in ordered Banach algebras.
Keywords: Ordered Banach spaces, Thompson metric, measure of noncompactness, fixed points
Herzog Gerd, Kunstmann Peer Christian: Kuratowski's Measure of Noncompactness with Respect to Thompson's Metric. Z. Anal. Anwend. 33 (2014), 335-346. doi: 10.4171/ZAA/1515