Continuous selections for metric projection operators and for their generalizations

DOI10.1070/IM8695zbMath1410.46007OpenAlexW2768415093MaRDI QIDQ4583576

I. G. Tsar'kov

Publication date: 31 August 2018

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

Full work available at URL: https://doi.org/10.1070/im8695

zbMATH Keywords

metric projectionpolyhedral spaceexistence setsemimetric spaceasymmetric spaces\(\varepsilon\)-selectioninfinitely connected setstrict solarity point

Mathematics Subject Classification ID

Set-valued and variational analysis (49J53) Selections in general topology (54C65) Geometry and structure of normed linear spaces (46B20) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (14)

Uniformly and locally convex asymmetric spaces ⋮ Continuity of a metric function and projection in asymmetric spaces ⋮ Some classical problems of geometric approximation theory in asymmetric spaces ⋮ Reflexivity for spaces with extended norm ⋮ Continuous selections of set-valued mappings and approximation in asymmetric and semilinear spaces ⋮ Density of the points of continuity of the metric function and projection in asymmetric spaces ⋮ Connectedness in asymmetric spaces ⋮ Existence, uniqueness, and stability of best and near-best approximations ⋮ Approximative properties of sets and continuous selections ⋮ Local approximation properties of sets and continuous selections on them ⋮ Uniform convexity in nonsymmetric spaces ⋮ Properties of monotone path-connected sets ⋮ Weakly monotone sets and continuous selection in asymmetric spaces ⋮ Monotone path-connectedness of Chebyshev sets in three-dimensional spaces

Cites Work

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• Connectedness and other geometric properties of suns and Chebyshev sets
• 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
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• Continuous \(\epsilon\)-selection and monotone path-connected sets
• 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 $
• Geometric Aspects of General Topology
• Continuous selection for set-valued mappings
• Topological Fixed Point Theory of Multivalued Mappings

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