Small sets in best approximation theory

被引：0
|
作者：
J. P. Revalski
N. V. Zhivkov
机构：
[1] Bulgarian Academy of Sciences,Institute of Mathematics and Informatics
来源：
Journal of Global Optimization | 2011年 / 50卷
关键词：
Best approximation; Metric projection; Well-posedness; Baire category; Porous sets; Cone supported sets; 41A65; 46B20;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The best approximation problem to a nonempty closed set in a locally uniformly convex Banach space is considered. The main result states that the set of points which have best approximation but the approximation problem is not well-posed is very small in a sense that it is σ-cone supported in the underlying space. This gives an improvement of an original result of Stečkin about the set of points with more than one best approximation which involves Baire categories. Examples on the necessity of some of the imposed conditions are provided.
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页码：77 / 91
页数：14
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