7 citations · 10 across the 6 of their papers we have counts for
6 papers
Chebyshev sets and ball operators
Horst Martini, Pedro Martín, Margarita Spirova
The Chebyshev set of a bounded set in a normed space is the set of centers of all minimal enclosing balls of . We use the concept of ball intersection and ball hull operator…
The 2-center problem and ball operators in strictly convex normed planes
Pedro Martín, Horst Martini, Margarita Spirova
We investigate the 2-center problem for arbitrary strictly convex, centrally symmetric curves instead of usual circles. In other words, we extend the 2-center problem (from the Euc…
On Bisectors in Normed Spaces
Thomas Jahn, Margarita Spirova
In this note, we completely describe the shape of the bisector of two given points in a two-dimensional normed vector space. More precisely, we show that, depending on the position…
Illuminating and covering convex bodies
Horst Martini, Christian Richter, Margarita Spirova
Covering numbers of convex bodies based on homothetical copies and related illumination numbers are well-known in combinatorial geometry and, for example, related to Hadwiger's fam…
Complete sets and completion of sets in Banach spaces
Horst Martini, Pier Luigi Papini, Margarita Spirova
In this paper we study properties of complete sets and of completions of sets in Banach spaces. We consider the family of completions of a given set and its size; we also study in…
Semi-inner products and the concept of semi-polarity
Ákos G. Horváth, Zsolt Lángi, Margarita Spirova
The lack of an inner product structure in Banach spaces yields the motivation to introduce a semi-inner product with a more general axiom system, one missing the requirement for sy…