# 47625

## Автор(ов):

1

Параметры публикации

## Тип публикации:

Статья в журнале/сборнике

## Название:

Inscribed Balls and Their Centers

0965-5425

## DOI:

10.1134/S0965542516100031

## Наименование источника:

• Computational Mathematics and Mathematical Physics

Vol. 57, No. 12

• Москва

2017

## Страницы:

1899-1907
Аннотация
A ball of maximal radius inscribed in a convex closed bounded set with a nonempty interior is considered in the class of uniformly convex Banach spaces. It is shown that, under certain conditions, the centers of inscribed balls form a uniformly continuous (as a set function) set-valued mapping in the Hausdorff metric. In a finite-dimensional space of dimension n, the set of centers of balls inscribed in polyhedra with a fixed collection of normals satisfies the Lipschitz condition with respect to sets in the Hausdorff metric. A Lipschitz continuous single-valued selector of the set of centers of balls inscribed in such polyhedra can be found by solving linear programming problems.

## Библиографическая ссылка:

Балашов М.В. Inscribed Balls and Their Centers // Computational Mathematics and Mathematical Physics. 2017. Vol. 57, No. 12. С. 1899-1907 .