Comparative properties of three metrics in the space of compact convex sets

被引：22

作者：

Diamond, P

Kloeden, P

Rubinov, A

Vladimirov, A

机构：

[1] Univ Queensland, Dept Math, St Lucia, Qld 4072, Australia

[2] Univ Ballarat, Sch Informat Technol & Math Sci, Ballarat, Vic 3353, Australia

[3] Univ Frankfurt, Fachbereich Math, D-60054 Frankfurt, Germany

[4] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow, Russia

来源：

SET-VALUED ANALYSIS | 1997年 / 5卷 / 03期

基金：

澳大利亚研究理事会;

关键词：

space of convex sets; Demyanov difference; Bartels-Pallaschke metric; derivative of set-valued function; convex fuzzy set;

D O I：

10.1023/A:1008667909101

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Along with the Hausdorff metric, we consider two other metrics on the space of convex sets, namely, the metric induced by the Demyanov difference of convex sets and the Bartels-Pallaschke metric. We describe the hierarchy of these three metrics and of the corresponding norms in the space of differences of sublinear functions. The completeness of corresponding metric spaces is demonstrated. Conditions of differentiability of convex-valued maps of one variable with respect to these metrics are proved for some special cases. Applications to the theory of convex fuzzy sets are given.

引用

页码：267 / 289

页数：23

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