Strong uniqueness and Lipschitz continuity of metric projections: A generalization of the classical Haar theory

DOI10.1016/0021-9045(89)90108-1zbMath0672.41026OpenAlexW2059123101MaRDI QIDQ1120091

Wu Li

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0021-9045(89)90108-1

zbMATH Keywords

Banach spacemetric projectionHaar condition

Mathematics Subject Classification ID

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

Related Items (7)

Error estimates and Lipschitz constants for best approximation in continuous function spaces ⋮ Continuities of metric projection and geometric consequences ⋮ Characterization of generalized Haar spaces ⋮ Uniform Hausdorff strong uniqueness ⋮ A relationship between the 1\(\frac12\)-ball property and the strong 1\(\frac12\)-ball property ⋮ Abadie's constraint qualification, Hoffman's error bounds, and Hausdorff strong unicity ⋮ Well-Posedness, Regularization, and Viscosity Solutions of Minimization Problems

Cites Work

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• Lipschitz conditions, strong uniqueness, and almost Chebyshev subspaces of C(X)
• Lipschitz continuity and strong unicity in G. Freud's work
• Local and global Lipschitz constants
• The set of continuous selections of a metric projection in C(X)
• Another characterization of Haar subspaces
• Unicity and strong unicity in approximation theory
• Uniqueness and strong uniqueness of best approximations by spline subspaces and other subspaces
• Continuity of the set-valued metric projection
• Some theorems on Cebysev approximation
• Uniqueness of Hahn-Banach Extensions and Unique Best Approximation
• Almost Čebyšev systems of continuous functions

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