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