Abstract
Abstract
Sets admitting a continuous selection of the operators of best and near-best approximation are studied. Michael’s classical continuous selection theorem is extended to the case of a lower semicontinuous metric projection in finite-dimensional spaces (with no a priori convexity conditions on its values). Sufficient conditions on the metric projection implying the solarity of the corresponding set are put forward in finite-dimensional polyhedral spaces. Available results for suns
are employed to establish the existence of continuous selections of the relative (with respect to
) Chebyshev near-centre map and of the sets of relative (with respect to
) near-Chebyshev points in certain classical spaces.
Bibliography: 30 titles.
Funder
Russian Foundation for Basic Research
Subject
Algebra and Number Theory
Cited by
26 articles.
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