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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Smoothness of certain metric projections on Hilbert space


Author: Richard B. Holmes
Journal: Trans. Amer. Math. Soc. 184 (1973), 87-100
MSC: Primary 41A65
MathSciNet review: 0326252
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Abstract: A study is made of differential properties of the distance function and the metric projection defined by a closed convex subset of Hilbert space. The former mapping is also considered within the context of more general Banach spaces.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0326252-2
PII: S 0002-9947(1973)0326252-2
Keywords: Best approximation, distance function, metric projection, Hilbert space, implicit function theorem, flat point
Article copyright: © Copyright 1973 American Mathematical Society