Approximation of continuous set-valued maps by constant set-valued maps with image balls
- Cite this article as:
- Dudov, S.I. & Konoplev, A.B. Math Notes (2007) 82: 469. doi:10.1134/S0001434607090222
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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.