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 Fundam. Prikl. Mat., 2018, Volume 22, Issue 1, Pages 99–110 (Mi fpm1782)

Criterion for the existence of a $1$-Lipschitz selection from the metric projection onto the set of continuous selections from a multivalued mapping

A. A. Vasil'eva

Lomonosov Moscow State University

Abstract: Let $S_F$ be the set of continuous bounded selections from the set-valued mapping $F\colon T \rightarrow 2^H$ with nonempty convex closed values; here $T$ is a paracompact Hausdorff topological space, and $H$ is a Hilbert space. In this paper, we obtain a criterion for the existence of a $1$-Lipschitz selection from the metric projection onto the set $S_F$ in $C(T,H)$.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-00295_à

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Citation: A. A. Vasil'eva, “Criterion for the existence of a $1$-Lipschitz selection from the metric projection onto the set of continuous selections from a multivalued mapping”, Fundam. Prikl. Mat., 22:1 (2018), 99–110

Citation in format AMSBIB
\Bibitem{Vas18} \by A.~A.~Vasil'eva \paper Criterion for the existence of a $1$-Lipschitz selection from the metric projection onto the set of continuous selections from a~multivalued mapping \jour Fundam. Prikl. Mat. \yr 2018 \vol 22 \issue 1 \pages 99--110 \mathnet{http://mi.mathnet.ru/fpm1782}