Geometry and topology of continuous best and near best approximations

JOURNAL OF APPROXIMATION THEORY

卷:105

Article

Kainen, PC ; Kürková, V ; Vogt, A

关键词: best approximation;    near best approximation;    continuous selection;    Chebyshev set;    strictly convex space;    uniformly convex space;    contractible set;    tangent hypercone;    modulus of convexity;    Chebyshev radius;   

DOI  :  10.1006/jath.2000.3467

来源: Elsevier

【 摘 要 】

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. (C) 2000 Academic Press.

【 授权许可】

Free