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.
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