B. B. Bednov, “The set of geometric medians for four-element subsets in Lindenstrauss spaces”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2019, Number 6,Pages <nobr>3

Mathematics

The set of geometric medians for four-element subsets in Lindenstrauss spaces

B. B. Bednov^ab

^a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b Bauman Moscow State Technical University

Abstract: We study the connection between the set of Steiner points for a four-element set and the set of Steiner points for a three-element subset in $L_1$-predual spaces. A Lipschitz selection is presented for the mapping from fours of continuous functions on a Hausdorff compact set to the set of their Steiner points.

Key words: Banach space, Lindenstrauss space, Steiner point, Lipschits selection.

UDC: 517.982.256+515.124.4

Received: 20.02.2019