The measure of nonconvexity and the jung constant

1996 ◽  
Vol 81 (2) ◽  
pp. 2562-2566 ◽  
Author(s):  
N. M. Gulevich
Keyword(s):  
Measure Of Nonconvexity ◽  
Jung Constant

Estimates for the Jung constant in Banach lattices

2000 ◽  
Vol 116 (1) ◽  
pp. 171-187 ◽  
Author(s):  
Jürgen Appell ◽  
Carlo Franchetti ◽  
Evgenij M. Semenov
Keyword(s):  
Banach Lattices ◽  
Jung Constant

Jung constant in ?1 n

1987 ◽  
Vol 42 (4) ◽  
pp. 787-791 ◽  
Author(s):  
V. L. Dol'nikov
Keyword(s):  
Jung Constant

Diametrically Maximal and Constant Width Sets in Banach Spaces

2006 ◽  
Vol 58 (4) ◽  
pp. 820-842 ◽  
Author(s):  
J. P. Moreno ◽  
P. L. Papini ◽  
R. R. Phelps
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Hausdorff Space ◽  
Constant Width ◽  
Negative Answer ◽  
Empty Interior ◽  
Finite Dimensional ◽  
Jung Constant

AbstractWe characterize diametrically maximal and constant width sets inC(K), whereKis any compact Hausdorff space. These results are applied to prove that the sum of two diametrically maximal sets needs not be diametrically maximal, thus solving a question raised in a paper by Groemer. A characterization of diametrically maximal sets inis also given, providing a negative answer to Groemer's problem in finite dimensional spaces. We characterize constant width sets inc0(I), for everyI, and then we establish the connections between the Jung constant of a Banach space and the existence of constant width sets with empty interior. Porosity properties of families of sets of constant width and rotundity properties of diametrically maximal sets are also investigated. Finally, we present some results concerning non-reflexive and Hilbert spaces.

An Estimate for the Measure of Nonconvexity in the Lp-Space

2004 ◽  
Vol 119 (2) ◽  
pp. 201-204 ◽  
Author(s):  
N. M. Gulevich ◽  
O. N. Gulevich
Keyword(s):  
Lp Space ◽  
Measure Of Nonconvexity

scholarly journals On properties of intersection of $\alpha$-sets

2020 ◽  
Vol 55 ◽  
pp. 79-92
Author(s):  
A.A. Ershov ◽  
O.A. Kuvshinov
Keyword(s):  
Experimental Study ◽  
Linear Function ◽  
Numerical Experiments ◽  
Convex Sets ◽  
Initial Value ◽  
Measure Of Nonconvexity ◽  
Simply Connected

In this paper, we study the properties of $\alpha$-sets, which are one of the generalizations of convex sets. In the first part of the paper, the equivalence of two definitions of $\alpha$-sets in the plane is proved. The second part of the work is devoted to the experimental study of the properties of simply connected intersections of $\alpha$-sets. It follows from the results of numerical experiments that the value $\alpha$ of the measure of nonconvexity in a simply connected intersection of two $\alpha$-sets can be greater than the initial value of $\alpha$ in intersected sets even when these values are very close to zero. Based on these results, we can hypothesize that, firstly, such an increase in the value of $\alpha$ is possible with an arbitrarily small initial $\alpha$ for intersected sets, secondly, this increase is limited by a linear function of the initial value of $\alpha$.

scholarly journals The separable Jung constant in Banach spaces

2020 ◽  
Author(s):  
Jesús M. F. Castillo ◽  
Pier Luigi Papini
Keyword(s):  
Banach Spaces ◽  
Jung Constant
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