Best approximation in

Authors:
R. Khalil and F. Saidi

Journal:
Proc. Amer. Math. Soc. **123** (1995), 183-190

MSC:
Primary 41A65; Secondary 46E40

DOI:
https://doi.org/10.1090/S0002-9939-1995-1223266-5

MathSciNet review:
1223266

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Abstract | References | Similar Articles | Additional Information

Abstract: Let *X* be a Banach space and *G* a closed subspace of *X*. The subspace *G* is called proximinal in *X* if for every there exists at least one such that .

It is an open problem whether is proximinal in if *G* is proximinal in *X*, where *I* is the unit interval with the Lebesgue measure.

In this paper, we prove the proximinality of in for a class of proximinal subspaces *G* in *X*.

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DOI:
https://doi.org/10.1090/S0002-9939-1995-1223266-5

Article copyright:
© Copyright 1995
American Mathematical Society