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Mat. Zametki, 2017, Volume 101, Issue 2, Pages 286–301 (Mi mz10972)  

This article is cited in 1 scientific paper (total in 1 paper)

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.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-3682.2014.1
Russian Foundation for Basic Research 15-01-08335
This work was supported by the Russian Foundation for Basic Research under grant 15-01-08335 and by the program “Leading Scientific Schools” under grant NSh-3682.2014.1.


DOI: https://doi.org/10.4213/mzm10972

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

Bibliographic databases:

UDC: 517.982.256
Received: 19.10.2015
Revised: 24.03.2016

Citation: A. A. Flerov, “Sets with at Most Two-Valued Metric Projection on a Normed Plane”, Mat. Zametki, 101:2 (2017), 286–301; Math. Notes, 101:2 (2017), 352–364

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Alimov A.R., Shchepin E.V., “Convexity of Suns in Tangent Directions”, Dokl. Math., 99:1 (2019), 14–15  crossref  isi
  • Математические заметки Mathematical Notes
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