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Carathéodory-type Theorems

✍ Scribed by Jürgen Bokowski; Javier Bracho; Ricardo Strausz

Publisher
Springer
Year
2010
Tongue
English
Weight
629 KB
Volume
45
Category
Article
ISSN
0179-5376

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📜 SIMILAR VOLUMES

Carathéodory's Theorem and H-Convexity
Carathéodory's Theorem and H-Convexity
✍ V. Boltyanski; H. Martini 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 165 KB

In 1976, V. Boltyanski introduced the functional md for compact, convex bodies. With the help of this functional, some theorems of combinatorial geometry were derived. For example, the first author obtained a Helly-type theorem, later some particular cases of the Szo kefalvi Nagy problem were resolv

A generalization of carathéodory's theor
A generalization of carathéodory's theorem
✍ Imre Bárány 📂 Article 📅 1982 🏛 Elsevier Science 🌐 English ⚖ 812 KB

The following theorem is lproved. If the sets VI, . . . , Vn+, CR" and a E fly:: conv Vi, then there exist elements ui E Vi (i = 1, . . . , n + 1) such that a E conv{o,, . . . , un+J. Thii is a generalization of Carathtidory's theorem. By applying this and similar results some open questions are ans