This article is cited in 3 papers

Approximation of Continuous Set-Valued Maps by Constant Set-Valued Maps with Image Balls

S. I. Dudov, A. B. Konoplev

Saratov State University named after N. G. Chernyshevsky

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.

Keywords: set-valued map, approximation of set-valued maps, Hausdorff metric, subdifferential, compact convex set.

UDC: 519.853

Received: 17.11.2006

DOI: 10.4213/mzm3809

 English version: Mathematical Notes, 2007, 82:4, 469–473

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