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Matematicheskie Zametki, 2010, Volume 87, Issue 4, Pages 514–518
DOI: https://doi.org/10.4213/mzm8697 (Mi mzm8697) 		 
This article is cited in 15 scientific papers (total in 15 papers)

An Example of Nonexistence of a Steiner Point in a Banach Space

P. A. Borodin

M. V. Lomonosov Moscow State University
Full-text PDF (349 kB) Citations (15)
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DOI: https://doi.org/10.4213/mzm8697
Abstract: For each $n=3,4,\dots$, we construct an example of a Banach space $X$ and elements $x_1,\dots,x_n$ in this space such that $X$ does not have any element with the minimal sum of distances to the elements $x_k$.
Keywords: Steiner point, Banach space, Hilbert space, reflexive space.
Received: 15.06.2009
Revised: 09.09.2009
English version:
Mathematical Notes, 2010, Volume 87, Issue 4, Pages 485–488
DOI: https://doi.org/10.1134/S0001434610030260
Bibliographic databases:
Document Type: Article
UDC: 517.982.256
Language: Russian
Citation: P. A. Borodin, “An Example of Nonexistence of a Steiner Point in a Banach Space”, Mat. Zametki, 87:4 (2010), 514–518; Math. Notes, 87:4 (2010), 485–488
Citation in format AMSBIB
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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