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On the size of approximately convex sets in normed spaces

100%

Dilworth S. J., Howard R., Roberts J. W.

Studia Mathematica

2000

tom 140

nr 3

213-241

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.

Composition operators on $F^{+}$

87%

Stoll M., Roberts J. W.

Studia Mathematica

1976

tom 57

nr 3

217-228

A compact convex set with no extreme points

62%

Roberts J. W.

Studia Mathematica

1977

tom 60

nr 3

255-266

Ograniczanie wyników

3 Studia Mathematica

3 Roberts J. W.

1 Dilworth S. J.

1 Howard R.

1 Stoll M.

1 2000

1 1977

1 1976

Wyniki wyszukiwania

On the size of approximately convex sets in normed spaces

Composition operators on $F^{+}$

A compact convex set with no extreme points