Geodesic
Criterion for the existence of a $1$-Lipschitz selection from the metric projection onto the set of continuous selections from a multivalued mapping
Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2018) no. 1, pp. 99-110 
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. Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2018) no. 1, pp. 99-110. http://geodesic.mathdoc.fr/item/FPM_2018_22_1_a4/
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     title = {Criterion for the existence of a $1${-Lipschitz} selection from the metric projection onto the set of continuous selections from a~multivalued mapping},
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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 $C(T,H)$.

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