Abstract:
We study the structural and approximative properties of closed spans in vector-valued function spaces. We consider the problems of existence and uniqueness of a best approximation of the space by closed spans and the stability of the metric projector.
\Bibitem{Vas04}
\by A.~A.~Vasil'eva
\paper Closed spans in vector-valued function spaces and their approximative properties
\jour Izv. Math.
\yr 2004
\vol 68
\issue 4
\pages 709--747
\mathnet{http://mi.mathnet.ru/eng/im496}
\crossref{https://doi.org/10.1070/IM2004v068n04ABEH000496}
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https://doi.org/10.1070/IM2004v068n04ABEH000496
https://www.mathnet.ru/eng/im/v68/i4/p75
This publication is cited in the following 15 articles:
A. R. Alimov, I. G. Tsar'kov, “Chebyshev centres, Jung constants, and their applications”, Russian Math. Surveys, 74:5 (2019), 775–849
I. G. Tsarkov, “Ustoichivost otnositelnogo chebyshëvskogo proektora v poliedralnykh prostranstvakh”, Tr. IMM UrO RAN, 24, no. 4, 2018, 235–245
A. A. Vasil'eva, “Criterion for the existence of a 11-Lipschitz selection from the metric projection onto the set of continuous selections from a multivalued mapping”, J. Math. Sci., 250:3 (2020), 454–462
A. R. Alimov, I. G. Tsar'kov, “Connectedness and solarity in problems of best and near-best approximation”, Russian Math. Surveys, 71:1 (2016), 1–77
A. R. Alimov, I. G. Tsar'kov, “Connectedness and other geometric properties of suns and Chebyshev sets”, J. Math. Sci., 217:6 (2016), 683–730
A. R. Alimov, “Monotone path-connectedness of RR-weakly convex sets in the space C(Q)C(Q)”, J. Math. Sci., 185:3 (2012), 360–366
A. R. Alimov, V. Yu. Protasov, “Separation of convex sets by extreme hyperplanes”, J. Math. Sci., 191:5 (2013), 599–604
A. R. Alimov, “Local solarity of suns in normed linear spaces”, J. Math. Sci., 197:4 (2014), 447–454
A. R. Alimov, “Bounded strict solar property of strict suns in the space C(Q)C(Q)”, Moscow University Mathematics Bulletin, 68:1 (2013), 14–17
Bednov B.B., “O tochkakh shteinera v prostranstve nepreryvnykh funktsii”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 2011, no. 6, 26–31
Steiner points in the space of continuous functions
B. B. Bednov, “Steiner points in the space of continuous functions”, Moscow Univ. Math. Bull., 66:6 (2011), 255
A. R. Alimov, “Preservation of approximative properties of Chebyshev sets and suns in a plane”, Moscow Univ. Math. Bull., 63:5 (2008), 198
A. A. Vasil'eva, “An Existence Criterion for a Smooth Function under Constraints”, Math. Notes, 82:3 (2007), 295–308
A. R. Alimov, “Monotone path-connectedness of Chebyshev sets in the space C(Q)C(Q)”, Sb. Math., 197:9 (2006), 1259–1272
A. R. Alimov, “Preservation of approximative properties of subsets
of Chebyshev sets and suns in ℓ∞(n)ℓ∞(n)”, Izv. Math., 70:5 (2006), 857–866
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