Geodesic
On the relation between $\alpha$-sets and weakly convex sets
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 4, pp. 276-285 Cet article a éte moissonné depuis la source Math-Net.Ru

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The known relation between $\alpha$-sets and Vial weakly convex sets in Euclidean spaces of dimension greater than two is strengthened. Namely, in the formula describing the relationship between nonconvexity measures for $\alpha$-sets and weakly convex sets, the double Chebyshev radius is replaced by the diameter of the set with a coefficient. However, in the two-dimensional space the corresponding estimate is expressed in terms of the set diameter without a coefficient and is more accurate. In this connection, the question of the possibility of further refinement of the estimate for the nonconvexity degree $\alpha$ in terms of the weak convexity parameter $R$ and the set diameter in Euclidean spaces of dimension greater than two remains open.
Mots-clés : $\alpha$-set
Keywords: weakly convex set, generalized convex set, diameter of a set, Chebyshev radius, convex hull. 
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V. N. Ushakov; A. A. Ershov. On the relation between $\alpha$-sets and weakly convex sets. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 4, pp. 276-285. http://geodesic.mathdoc.fr/item/TIMM_2024_30_4_a21/

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