A survey of metric selections

DOI10.1090/conm/018/728593zbMath0518.41030OpenAlexW4231513479MaRDI QIDQ3667355

Frank Deutsch

Publication date: 1983

Published in: Fixed Points and Nonexpansive Mappings (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/conm/018/728593

zbMATH Keywords

proximinal spacemetric selections

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Research exposition (monographs, survey articles) pertaining to approximations and expansions (41-02) Nonlinear operators and their properties (47H99) Approximation by arbitrary linear expressions (41A45)

Related Items (24)

Stability estimates of continuous selections for metric almost-projections ⋮ Continuous selections for the metric projection on \(C_ 1\) ⋮ Lipschitzian selections in approximation from nonconvex sets of bounded functions ⋮ Set valued mappings, continuous selections, and metric projections ⋮ Piecewise linear approximations of set-valued maps ⋮ An equivalent condition of continuous metric selection ⋮ Continuous metric selection and multivariate approximation ⋮ Lipschitzian selections in best approximation by continuous functions ⋮ Uniform approximation by quasi-convex and convex functions ⋮ Characterizations of continuous and Lipschitz continuous metric selections in normed linear spaces ⋮ New results in the theory of multivalued mappings. I: Topological characteristics and solvability of operator relations ⋮ Ernest Michael and theory of continuous selections ⋮ Duality and Lipschitzian selections in best approximation from nonconvex cones ⋮ Rigidity properties of nonexpansive mappings ⋮ Uniform approximation by a non-convex cone of continuous functions ⋮ The metric projection for free knot splines ⋮ Best approximation by integer-valued functions ⋮ Continuous selections for metric projections in spaces of continuous functions and a disjoint leaves condition ⋮ An intrinsic characterization of lower semicontinuity of the metric projection in \(C_ 0(T,X)\) ⋮ Various continuities of metric projections in \(C_ 0(T,X)\) ⋮ A relationship between the 1\(\frac12\)-ball property and the strong 1\(\frac12\)-ball property ⋮ Nonuniqueness and selections in spline approximation ⋮ Remarks on linear selections for the metric projection ⋮ On continuity and selections of multifunctions

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