An Example of a Banach Space with Non-Lipschitzian Metric Projection on Any Straight Line

L. Sh. Burusheva

Moscow Center for Fundamental and Applied Mathematics

Abstract: We construct an example of a three-dimensional strictly convex normed space on which the operator of metric projection onto any straight line does not satisfy the Lipschitz condition.

Keywords: Banach space, metric projection, Chebyshev set, Lipschitz condition.

UDC: 517.982.256

Received: 20.03.2019
Revised: 16.09.2020

DOI: 10.4213/mzm12383

 English version: Mathematical Notes, 2021, 109:2, 184–191

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