- Tytuł:
- On the size of approximately convex sets in normed spaces
- Autorzy:
-
Dilworth, S. J.
Howard, Ralph
Roberts, James W. - Powiązania:
- https://bibliotekanauki.pl/articles/1206043.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Opis:
- Let X be a normed space. A set A ⊆ X is approximately convex} if d(ta+(1-t)b,A)≤1 for all a,b ∈ A and t ∈ [0,1]. We prove that every n-dimensional normed space contains approximately convex sets A with $ℋ(A,Co(A))≥log_2n-1$ and $diam(A)≤C√n(ln n)^2$, where ℋ denotes the Hausdorff distance. These estimates are reasonably sharp. For every D>0, we construct worst possible approximately convex sets in C[0,1] such that ℋ(A,Co(A))=(A)=D. Several results pertaining to the Hyers-Ulam stability theorem are also proved.
- Źródło:
-
Studia Mathematica; 2000, 140, 3; 213-241
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł