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.
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Original Russian Text © S. I. Dudov, A. B. Konoplev, 2007, published in Matematicheskie Zametki, 2007, Vol. 82, No. 4, pp. 525–529.
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Dudov, S.I., Konoplev, A.B. Approximation of continuous set-valued maps by constant set-valued maps with image balls. Math Notes 82, 469–473 (2007). https://doi.org/10.1134/S0001434607090222
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DOI: https://doi.org/10.1134/S0001434607090222