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Inscribed centers, reflexivity, and some applications
Published online by Cambridge University Press: 09 April 2009
Abstract
We first define an inscribed center of a bounded convex body in a normed linear space as the center of a largest open ball contained in it (when such a ball exists). We then show that completeness is a necessary condition for a normed linear space to admit inscribed centers. We show that every weakly compact convex body in a Banach space has at least one inscribed center, and that admitting inscribed centers is a necessary and sufficient condition for reflexivity. We finally apply the concept of inscribed center to prove a type of fixed point theorem and also deduce a proposition concerning so-called Klee caverns in Hilbert spaces.
MSC classification
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 41 , Issue 3 , December 1986 , pp. 317 - 324
- Copyright
- Copyright © Australian Mathematical Society 1986
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