Approximation of continuous set-valued maps by constant set-valued maps with image balls

被引：3

作者：

Dudov, S. I. ^{[1
]}

Konoplev, A. B. ^{[1
]}

机构：

[1] Saratov NG Chernyshevskii State Univ, Saratov, Russia

来源：

MATHEMATICAL NOTES | 2007年 / 82卷 / 3-4期

关键词：

set-valued map; approximation of set-valued maps; Hausdorff metric; subdifferential; compact convex set;

D O I：

10.1134/S0001434607090222

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is shown that the problem of the best uniform approximatiou in the Hausdorff metric Of a continous set-valued map with finite-dimensional compact convex images by constant set-valued maps whose images are balls in some norm can be reduced to a Visual geometric problem. The latter consists in constructing a spherical layer of minimal thickness which contains the complement of a compact convex set to a larger compact convex set.

引用

页码：469 / 473

页数：5

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