Radial continuity of set-valued metric projections

DOI10.1016/0021-9045(74)90016-1zbMath0283.41014OpenAlexW1967377637MaRDI QIDQ1844396

Bruno Brosowski, Frank Deutsch

Publication date: 1974

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9045(74)90016-1

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (15)

A monotone path-connected set with outer radially lower continuous metric projection is a strict sun ⋮ Connectedness and other geometric properties of suns and Chebyshev sets ⋮ Continuity of the metric projection and local solar properties of sets. Continuity of the metric projection and local solar properties of sets, continuity of the metric projection and solar properties ⋮ Continuous selections for the metric projection and alternation ⋮ Selections of the metric projection operator and strict solarity of sets with continuous metric projection ⋮ Characterization of sets with continuous metric projection in the space \(\ell^\infty_n\) ⋮ Support cones and convexity of sets in ℝⁿ ⋮ The metric projection for free knot splines ⋮ The continuity of the metric projection on a subspace of finite codimension in the space of continuous functions ⋮ Approximate selections, best approximations, fixed points, and invariant sets ⋮ Strict sums and semicontinuity below metric projections in linear normed spaces ⋮ Variation of the norms in the problem of best approximation ⋮ On continuity of metric projections ⋮ Stability of best rational Chebyshev approximation ⋮ Continuity of metric projection

Cites Work

• On the lower semicontinuity of the set-valued metric projection
• On some geometric properties of suns
• Chebyshev sets and approximately convex sets
• Metric projections onto subspaces of finite codimension
• Continuity of the set-valued metric projection
• Charakterisierung bester Approximationen in normierten Vektorräumen
• Über eine Fixpunkteigenschaft der metrischen Projektion
• Suns, moons, and quasi-polyhedra
• Best n -Dimensional Approximation to Sets of Functions
• Extension of compact operators
• Continuity of Metric Projections
• Cebysev Sets in Hilbert Space
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