This article is cited in 3 papers

Sets with at Most Two-Valued Metric Projection on a Normed Plane

A. A. Flerov

Lomonosov Moscow State University

Abstract: We study sets with at most two-valued metric projection in Banach spaces. We show that a two-dimensional Banach space is smooth if and only if every point of the convex hull of an arbitrary closed set with at most two-valued metric projection lies on a segment with endpoints in that set.

Keywords: metric projection, set with at most two-valued metric projection.

UDC: 517.982.256

Received: 19.10.2015
Revised: 24.03.2016

DOI: 10.4213/mzm10972

 English version: Mathematical Notes, 2017, 101:2, 352–364

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