It is known that the interior of a normal cone in a Banach space is a complete metric space with respect to Thompson's metric . We prove that Kuratowski's measure of noncompactness 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 partly differ to the classical case. Among others is nicely compatible with the multiplication in ordered Banach algebras.
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Gerd Herzog, Peer Christian Kunstmann, Kuratowski's Measure of Noncompactness with Respect to Thompson's Metric. Z. Anal. Anwend. 33 (2014), no. 3, pp. 335–346DOI 10.4171/ZAA/1515