Some classical problems of geometric approximation theory in asymmetric spaces

DOI10.1134/S000143462207001XOpenAlexW4293373962WikidataQ114075380 ScholiaQ114075380MaRDI QIDQ2170483

I. G. Tsar'kov, Alexey R. Alimov

Publication date: 6 September 2022

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s000143462207001x

zbMATH Keywords

fixed pointcontinuous selectionapproximatively compact setsunasymmetric space

Mathematics Subject Classification ID

Normed linear spaces and Banach spaces; Banach lattices (46Bxx) Approximations and expansions (41Axx) Maps and general types of topological spaces defined by maps (54Cxx)

Related Items (3)

Existence, uniqueness, and stability of best and near-best approximations ⋮ Kuhn-Tucker type theorems in cone and linear normed spaces ⋮ Strict protosuns in asymmetric spaces of continuous functions

Cites Work

• Properties of sets admitting stable \(\varepsilon \)-selections
• Uniqueness of circumcenters in generalized Minkowski spaces
• Uniform convexity in nonsymmetric spaces
• Compact bilinear operators on asymmetric normed spaces
• Ball-complete sets and solar properties of sets in asymmetric spaces
• Characterization of sets with continuous metric projection in the space \(\ell^\infty_n\)
• Index of symmetry and topological classification of asymmetric normed spaces
• Local approximation properties of sets and continuous selections on them
• Convexity of Chebyshev sets contained in a subspace
• Smoothness of subspace sections of the unit balls of \(C(Q)\) and \(L^1\)
• \(\mathring{B}\)-complete sets: approximative and structural properties
• Connectedness and solarity in problems of best and near-best approximation
• Local and global continuous $ \varepsilon$-selection
• Functional Analysis in Asymmetric Normed Spaces
• APPROXIMATIVE PROPERTIES OF SETS IN NORMED LINEAR SPACES
• Continuous selections for metric projection operators and for their generalizations
• Selections of the metric projection operator and strict solarity of sets with continuous metric projection
• Separation axioms and covering dimension of asymmetric normed spaces
• Approximative properties of sets and continuous selections

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