Mathematical Notes

, Volume 82, Issue 3–4, pp 469–473

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

Mathematical Notes

DOI: 10.1134/S0001434607090222

Cite this article as:
Dudov, S.I. & Konoplev, A.B. Math Notes (2007) 82: 469. doi:10.1134/S0001434607090222


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.

Key words

set-valued map approximation of set-valued maps Hausdorff metric subdifferential compact convex set 

Copyright information

© Pleiades Publishing, Ltd. 2007

Authors and Affiliations

  1. 1.Saratov State UniversityRussia

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