JournalszaaVol. 33, No. 3pp. 335–346

Kuratowski's Measure of Noncompactness with Respect to Thompson's Metric

  • Gerd Herzog

    Karlsruher Institut für Technologie (KIT), Germany
  • Peer Christian Kunstmann

    Karlsruher Institut für Technologie (KIT), Germany
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Abstract

It is known that the interior of a normal cone KK in a Banach space is a complete metric space with respect to Thompson's metric dd. We prove that Kuratowski's measure of noncompactness τ\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 τ\tau partly diff er to the classical case. Among others τ\tau is nicely compatible with the multiplication in ordered Banach algebras.

Cite this article

Gerd Herzog, Peer Christian Kunstmann, Kuratowski's Measure of Noncompactness with Respect to Thompson's Metric. Z. Anal. Anwend. 33 (2014), no. 3, pp. 335–346

DOI 10.4171/ZAA/1515