Differentiability of Distance Functions and a Proximinal Property Inducing Convexity

DOI10.2307/2046995zbMath0692.41036OpenAlexW4234485097MaRDI QIDQ3034294

John R. Giles

Publication date: 1988

Full work available at URL: https://doi.org/10.2307/2046995

zbMATH Keywords

distance functionChebyshev setsuniformly Gâteaux differentiablemetric projectionuniformly Fréchet differentiableFréchetGâteauxstrong differentiabilityproximinal

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (6)

Convex analysis in normed spaces and metric projections onto convex bodies ⋮ On closures of preimages of metric projection mappings in Hilbert spaces ⋮ Differential properties of the Moreau envelope ⋮ Proximality and Chebyshev sets ⋮ A distance function property implying differentiability ⋮ Differentiability of distance function and the proximinal condition implying convexity

Cites Work

• The differentiability of real functions on normed linear space using generalized subgradients
• Dispersed Chebyshev sets and coverings by balls
• A rotund reflexive space having a subspace of codimension two with a discontinuous metric projection
• Almost convex and Chebyshev sets
• Differentiation of Real-Valued Functions and Continuity of Metric Projections
• The Proximal Normal Formula in Banach Space
• Metric projections and the differentiability of distance functions
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