47625

Автор(ы): 

Автор(ов): 

1

Параметры публикации

Тип публикации: 

Статья в журнале/сборнике

Название: 

Inscribed Balls and Their Centers

ISBN/ISSN: 

0965-5425

DOI: 

10.1134/S0965542516100031

Наименование источника: 

  • Computational Mathematics and Mathematical Physics

Обозначение и номер тома: 

Vol. 57, No. 12

Город: 

  • Москва

Издательство: 

  • Pleiadis publishing, Ltd.

Год издания: 

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 .