Vol. 35, No. 3, 1970

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Characterization of the Steiner point

Walter J. Meyer

Vol. 35 (1970), No. 3, 717–725
Abstract

Let f be a mapping which associates with each compact convex set in En a point of En. If f is linear (in terms of the vector addition of convex sets), uniformly continuous and commutes with a substantial enough set of congruences of En, then f(K) is the Steiner point of K for all compact convex sets K.

Mathematical Subject Classification
Primary: 52.30
Milestones
Received: 20 October 1969
Published: 1 December 1970
Authors
Walter J. Meyer