The Mapping Taking Three Points of a Banach Space to their Steiner Point / K. V. Chesnokova. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2016. ¹ 2. P. 40-44 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 71-74].

A mapping \mathrm{St} taking any three points a, b, c of a Banach space X into a set \mathrm{St}(a, b, c) of their Steiner points and the 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 an arbitrary selection from P_D is estimated depending on properties of the space X. Estimates for the Lipschitz constant of an arbitrary selection from the mapping \mathrm{St} are obtained as a corollary.

Key words: the linearity coefficient of metric projections, median.