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On strict suns in $\ell^\infty(3)$

A. R. Alimov
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Abstract

A subset M of a normed linear space X is said to be a {\it strict sun} if, for every point $x\in X\setminus M$, the set of its nearest points from~$M$ is non-empty and if $y\in M$ is a nearest point from M to x, then y is a nearest point from M to all points from the ray $\{λx+(1- λ)y | λ>0\}$. In the paper there obtained a geometrical characterisation of strict suns in $\ell^\infty(3)$.

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BibTeXRIS

A. R. Alimov. 2002-05-27. On strict suns in $\ell^\infty(3)$. https://arxiv.org/abs/math/0205280

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