measure of nonconvexity
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2020 ◽  
Vol 55 ◽  
pp. 79-92
Author(s):  
A.A. Ershov ◽  
O.A. Kuvshinov

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 $\alpha$.


2004 ◽  
Vol 119 (2) ◽  
pp. 201-204 ◽  
Author(s):  
N. M. Gulevich ◽  
O. N. Gulevich

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