On convex and strongly convex approximations of sets (Q1385873)

It is shown that the totality of all strongly convex sets is invariant under linear operations and the passage to the limit in the Hausdorff metric. The concept of a strongly convex hull is defined, and its properties are studied. With the help of support functions, approximations of convex solid compact sets, including strongly convex sets, by polyhedrons or other strongly convex sets are considered, and error estimates for these approximations are obtained, which depend on the net that defines the polyhedron.