The Steiner Mapping for Three Points in Euclidean Plane

For the Euclidean plane ? the Steiner mapping associating any three points a, b, c with their median s, and the corresponding operator P _D of metric projection of the space l ₁ ³ (?) onto its diagonal subspace D = {(x,x,x): x ∈ ?}, P _D (a,b,c) = (s,s,s): s are considered. The exact value of the linearity coefficient of P _D is calculated.