Journal of the Australian Mathematical Society | |
Inscribed centers, reflexivity, and some applications | |
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
【 预 览 】
Files | Size | Format | View |
---|---|---|---|
RO201912040543866ZK.pdf | 297KB | download |