Example of an antiproximinal, but not a 2-antiproximinal convex closed bounded body.

DOI10.3103/S0027132216050077zbMath1379.46017OpenAlexW2556158633MaRDI QIDQ2364170

Borislav Borisovich Bednov

Publication date: 18 July 2017

Published in: Moscow University Mathematics Bulletin (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s0027132216050077

zbMATH Keywords

Banach spacebest approximationmetric projectionproximinal setantiproximinal setlocally uniformly convex space

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Cites Work

• The \(n\)-antiproximinal sets
• Antiproximinal convex bounded sets in the space \(c_{0}(\gamma )\) equipped with the Day norm
• Convex antiproximinal sets in spaces \(c_0\) and \(c\)
• Antiproximal sets
• Some results on nearest points and support properties of convex sets in \(c_ 0\)
• On the convexity of $ N$-Chebyshev sets
• Strict Convexity and Smoothness of Normed Spaces

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