Generalized convex sets and the problem of shadow
The problem of shadow is solved. It is equivalent to the problem of finding conditions for a point to belong to a generalized convex hull of a family of compact sets.
Citation Example: Stefanchuk M. V., Vyhovs'ka I. Yu., Zelinskii Yu. B. Generalized convex sets and the problem of shadow // Ukr. Mat. Zh. - 2015. - 67, № 12. - pp. 1658-1666.