Strong uniqueness, Lipschitz continuity, and continuous selections for metric projections in \(L_1\)

DOI10.1016/0021-9045(91)90121-PzbMath0737.41035OpenAlexW2086661423MaRDI QIDQ1176142

Wu Li, Frank Deutsch

Publication date: 25 June 1992

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

Full work available at URL: https://doi.org/10.1016/0021-9045(91)90121-p

zbMATH Keywords

metric projectionLyapunov convexity theorem

Mathematics Subject Classification ID

Set-valued maps in general topology (54C60) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) (54C55)

Related Items (4)

Continuities of metric projection and geometric consequences ⋮ Existence of Lipschitz selections of the Steiner map ⋮ Uniqueness of minimal Fourier-type extensions in \(L_1\)-spaces ⋮ Lipschitz selections of set-valued mappings and Helly's theorem

Cites Work

• Continuous selections. I
• Some characterizations of convex polyhedra
• Characterizations of continuous and Lipschitz continuous metric selections in normed linear spaces
• Linear selections for the metric projection
• Remarks on linear selections for the metric projection
• Lipschitz continuity and strong unicity in G. Freud's work
• Continuous selections for the metric projection on \(C_ 1\)
• Lower semicontinuity, almost lower semicontinuity, and continuous selections for set-valued mappings
• Eindeutigkeit in der \(L_1\)-Approximation
• On Lipschitz conditions, strong unicity and a theorem of A. K. Cline
• Strong uniqueness: A far-reaching criterion for the convergence analysis of iterative procedures
• Various continuities of metric projections in \(C_ 0(T,X)\)
• Uniform Hausdorff strong uniqueness
• Connectedness properties of the range of vector and semimeasures
• Lipschitz conditions on uniform approximation operators
• Dual convex polytopes in Banach spaces
• Uniqueness of Hahn-Banach Extensions and Unique Best Approximation
• Strong unicity of best approximations : A numerical aspect
• A Theorem on Weighted L 1 -Approximation
• Approximation in the Metric of L 1 (X,μ)
• Cebysev Subspaces of Finite Dimension in L 1
• Spaces of Affine Continuous Functions on Simplexes
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