A distance function property implying differentiability

DOI10.1017/S0004972700027982zbMath0689.46003MaRDI QIDQ3031471

John R. Giles

Publication date: 1989

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

distance function propertyuniformly Gâteaux (uniformly Fréchet) differentiable norm

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 (10)

Subdifferentials of distance function outside of target set in Riemannian manifolds ⋮ Convexity of generalized proximinal sets in Banach spaces ⋮ Convex analysis in normed spaces and metric projections onto convex bodies ⋮ On closures of preimages of metric projection mappings in Hilbert spaces ⋮ Limiting subdifferentials of perturbed distance functions in Banach spaces ⋮ Differential properties of the Moreau envelope ⋮ Subdifferentials of perturbed distance function in Riemannian manifolds ⋮ Differentiability of distance function and the proximinal condition implying convexity ⋮ Generalized derivatives of distance functions and the existence of nearest points ⋮ Derivatives of generalized distance functions and existence of generalized nearest points

Cites Work

• The differentiability of real functions on normed linear space using generalized subgradients
• Weakly proximinal sets
• Chebyshev sets and approximately convex sets
• Almost convex and Chebyshev sets
• Differentiability of Distance Functions and a Proximinal Property Inducing Convexity
• Differentiation of Real-Valued Functions and Continuity of Metric Projections
• The Proximal Normal Formula in Banach Space
• A Smooth Variational Principle With Applications to Subdifferentiability and to Differentiability of Convex Functions
• Generalized Gradients and Applications

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