Continuous selection from the sets of best and near-best approximation

DOI10.1134/S1064562417040196zbMath1401.41023OpenAlexW2752825417MaRDI QIDQ2411800

I. G. Tsar'kov

Publication date: 25 October 2017

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562417040196

zbMATH Keywords

normed linear spaceapproximation theory\(\varepsilon\)-selectionasymmetric space

Mathematics Subject Classification ID

Set-valued maps in general topology (54C60) Selections in general topology (54C65) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (5)

Selections of the best and near-best approximation operators and solarity ⋮ Weakly monotone sets and continuous selection from a near-best approximation operator ⋮ Approximative properties of sets and continuous selections ⋮ New criteria for the existence of a continuous \(\epsilon\)-selection ⋮ Weakly monotone sets and continuous selection in asymmetric spaces

Cites Work

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• Relations between certain classes of sets in Banach spaces
• Properties of sets admitting stable \(\varepsilon \)-selections
• Continuous selections. I
• Properties of sets that have a continuous selection of the operator \(P^{\delta}\)
• Uniform continuity of generalized rational approximations
• Continuity of operators of generalized rational approximation in the space \(L_1[0;1\)]
• Continuous ε-selection
• Connectedness and solarity in problems of best and near-best approximation
• Local and global continuous $ \varepsilon$-selection
• Monotone path-connectedness of Chebyshev sets in the space $ C(Q)$
• Stability of the operator of $ \varepsilon$-projection to the set of splines in $ C \lbrack 0,1 \rbrack $
• Topological Fixed Point Theory of Multivalued Mappings

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