Inscribed centers, reflexivity, and some applications

Journal of the Australian Mathematical Society

A. A. Astaneh¹ 

关键词: 46 B 20;    46 B 10;    47 H 10;   

DOI  :  10.1017/S1446788700033759

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

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.

【 授权许可】

Unknown