Geometry and Topology of Continuous Best and Near Best Approximations

0403663 - UIVT-O 20000019 RIV US eng J - Journal Article
Kainen, P.C. - Kůrková, Věra - Vogt, A.
Geometry and Topology of Continuous Best and Near Best Approximations.
Journal of Approximation Theory. Roč. 105, č. 2 (2000), s. 252-262. ISSN 0021-9045. E-ISSN 1096-0430
R&D Projects: GA ČR GA201/99/0092; GA AV ČR IAA2030602; GA ČR GA201/00/1489
Institutional research plan: AV0Z1030915
Keywords : best approximation * near best approximation * continuous selection * Chebyshev set * strictly convex space * uniformly convex space * conctraible set * tangent hypercone * modulus of convexity * Chebyshev radius
Subject RIV: BA - General Mathematics
Impact factor: 0.556, year: 2000

The existence of a continuous best approximation or of near best approximations of a strictly convex space by a subset is shown to imply uniqueness of the best approximation under various assumptions on the approximating subset. For more general spaces, when continuous best or near best approximations exist, the set of best approximants to any given element is shown to satisfy connectivity and radius constraints.
Permanent Link: http://hdl.handle.net/11104/0123961