Abstract:
Finite-dimensional problems of finding outer, inner, and uniform estimates
for a convex compactum by a ball in an arbitrary norm are considered and
compared, as well as the problem of finding estimates
of the boundary
of a convex compactum by a spherical annulus of the smallest width.
It is shown that these problems can be linked
by means of the parametric problem of finding
the best approximation in the Hausdorff metric of
the compactum under consideration by a ball of fixed radius.
One can indicate ranges of the fixed radius in which solutions of
the latter problem give solutions of the problems mentioned above.
However, for some values of the radius this latter problem can be
independent.
Bibliography: 12 titles.
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