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Matematicheskie Zametki, 2021, Volume 109, Issue 2, Pages 196–205
DOI: https://doi.org/10.4213/mzm12383 (Mi mzm12383) 		 
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
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DOI: https://doi.org/10.4213/mzm12383
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.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00333-а
Ministry of Education and Science of the Russian Federation НШ-6222.2018.1
Foundation for the Development of Theoretical Physics and Mathematics BASIS
This work was supported by the Russian Foundation for Basic Research under grant 18-01-00333-a, by the program “Leading Scientific Schools” under grant NSh-6222.2018.1, and by the Foundation “BASIS” for Development of Theoretical Physics and Mathematics.
Received: 20.03.2019
Revised: 16.09.2020
English version:
Mathematical Notes, 2021, Volume 109, Issue 2, Pages 184–191
DOI: https://doi.org/10.1134/S0001434621010223
Bibliographic databases:
Document Type: Article
UDC: 517.982.256
Language: Russian
Citation: L. Sh. Burusheva, “An Example of a Banach Space with Non-Lipschitzian Metric Projection on Any Straight Line”, Mat. Zametki, 109:2 (2021), 196–205; Math. Notes, 109:2 (2021), 184–191
Citation in format AMSBIB
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