Geodesic
The mapping taking three points of a Banach space to their Steiner point
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2016), pp. 40-44 
K. V. Chesnokova. The mapping taking three points of a Banach space to their Steiner point. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2016), pp. 40-44. http://geodesic.mathdoc.fr/item/VMUMM_2016_2_a6/
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     author = {K. V. Chesnokova},
     title = {The mapping taking three points of a {Banach} space to their {Steiner} point},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {40--44},
     year = {2016},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2016_2_a6/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A mapping $\mathrm{St}$ sending any three points $a, b, c$ of a Banach space $X$ into a set $\mathrm{St}(a, b, c)$ of their medians and a corresponding operator $P_D$ of metric projection of a space $X \times X \times X$ onto its diagonal subspace $D=\{(x, x, x) \colon x \in X\}$, $P_D(a, b, c)=\{(s, s, s) \colon s \in \mathrm{St}(a, b, c)\}$, are considered. The linearity coefficient of arbitrary selection from $P_D$ is estimated, depending on different properties of the space $X$. As a corollary, estimates for the Lipschitz constant of arbitrary selection from the mapping $\mathrm{St}$ are obtained.

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