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.
Citation:
S. I. Dudov, A. B. Konoplev, “Approximation of Continuous Set-Valued Maps by Constant Set-Valued Maps with Image Balls”, Mat. Zametki, 82:4 (2007), 525–529; Math. Notes, 82:4 (2007), 469–473
This publication is cited in the following 3 articles:
Neufeld A., Sester J., “On the Stability of the Martingale Optimal Transport Problem: a Set-Valued Map Approach”, Stat. Probab. Lett., 176 (2021), 109131
S. I. Dudov, E. V. Sorina, “Uniform estimate for a segment function in terms of a polynomial strip”, St. Petersburg Math. J., 24:5 (2013), 723–742
S. I. Dudov, E. V. Sorina, “Uniform estimation of a segment function by a polynomial strip of fixed width”, Comput. Math. Math. Phys., 51:11 (2011), 1864–1877