, Volume 82, Issue 3-4, pp 469-473

Approximation of continuous set-valued maps by constant set-valued maps with image balls

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Abstract

It is shown that the problem of the best uniform approximation in the Hausdorff metric of a continuous set-valued map with finite-dimensional compact convex images by constant set-valued maps whose images are balls in some norm can be reduced to a visual geometric problem. The latter consists in constructing a spherical layer of minimal thickness which contains the complement of a compact convex set to a larger compact convex set.

Original Russian Text © S. I. Dudov, A. B. Konoplev, 2007, published in Matematicheskie Zametki, 2007, Vol. 82, No. 4, pp. 525–529.