Geodesic
An Example of Nonexistence of a Steiner Point in a Banach Space
Matematičeskie zametki, Tome 87 (2010) no. 4, pp. 514-518.

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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. 
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     author = {P. A. Borodin},
     title = {An {Example} of {Nonexistence} of a {Steiner} {Point} in a {Banach} {Space}},
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P. A. Borodin. An Example of Nonexistence of a Steiner Point in a Banach Space. Matematičeskie zametki, Tome 87 (2010) no. 4, pp. 514-518. http://geodesic.mathdoc.fr/item/MZM_2010_87_4_a3/

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