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Strongly unique best approximation in Banach spaces. II. (English) Zbl 0657.41022
The author continues his study of strongly unique best approximation initiated in a previous paper under the same title [J. Approximation Theory 47, 184-194 (1986; Zbl 0615.41027)]. He shows that a best approximation by elements of a sun in a uniformly convex Banach space is strongly unique locally, and gives the global analogies also. He applies the latter results to derive strong uniqueness theorems for Lebesgue, Hardy and Sobolev spaces.
Reviewer: S.Aljančić

MSC:
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
41A50 Best approximation, Chebyshev systems
Citations:
Zbl 0615.41027
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