The mapping taking three points of a Banach space to their Steiner point

A mapping St taking any three points a, b, c of a Banach space X into a set St(a,b,c) of their Steiner points and the corresponding operator P D of metric projection of a space X × X × X onto its diagonal subspace D = {(x,x,x): x ∈ X}, P D (a,b,c) = {(s,s,s): s ∈ 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 St are obtained as a corollary.