Metric Curvature, Folding, and Unique Best Approximation
- 1 May 1976
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 7 (3) , 436-449
- https://doi.org/10.1137/0507035
Abstract
In this paper, the concepts of metric curvature and folding of a $C^1 $-representable manifold in a normed linear space are studied. With certain restrictions on the metric curvature and/or folding, one can obtain a neighborhood of unique best approximation from the manifold, and in some cases, the manifold can be shown to be Chebyshev. Several familiar examples, including some classes of $\gamma $-polynomials, are given.Keywords
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