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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{VMUMM_2016_2_a6,
     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/}
}
TY  - JOUR
AU  - K. V. Chesnokova
TI  - The mapping taking three points of a Banach space to their Steiner point
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2016
SP  - 40
EP  - 44
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2016_2_a6/
LA  - ru
ID  - VMUMM_2016_2_a6
ER  - 
%0 Journal Article
%A K. V. Chesnokova
%T The mapping taking three points of a Banach space to their Steiner point
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2016
%P 40-44
%N 2
%U http://geodesic.mathdoc.fr/item/VMUMM_2016_2_a6/
%G ru
%F VMUMM_2016_2_a6
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/

[1] Garkavi A.L., Shmatkov V.A., “O tochke Lame i ee obobscheniyakh v normirovannom prostranstve”, Matem. sb., 95(137):2(10) (1974), 272–293 | MR | Zbl

[2] Rubinshtein G.Sh., “Ob odnoi ekstremalnoi zadache v lineinom normirovannom prostranstve”, Sib. matem. zhurn., VI:3 (1965), 711–714 | Zbl

[3] Borodin P.A., “Koeffitsient lineinosti operatora metricheskogo proektirovaniya na chebyshevskoe podprostranstvo”, Matem. zametki, 85:2 (2009), 180-188 | DOI | Zbl

[4] Distel Dzh., Geometriya banakhovykh prostranstv, Vischa shkola, Kiev, 1980 | MR

[5] Kahane J.-P., “Best approximation in $L^1(T)$”, Bull. Amer. Math. Soc., 80:5 (1974), 788–804 | DOI | MR | Zbl