Differentiability of distance function and the proximinal condition implying convexity

DOI10.1007/s41478-020-00259-5zbMath1477.46049arXiv1504.07292OpenAlexW3044902227MaRDI QIDQ2026947

Triloki Nath

Publication date: 21 May 2021

Published in: The Journal of Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.07292

zbMATH Keywords

differentiabilitydistance functionChebyshev setgeneralized subdifferentialproximinal setalmost sun

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) Derivatives of functions in infinite-dimensional spaces (46G05)

Related Items (3)

On local properties of spaces implying monotone path-connectedness of suns ⋮ Approximatively compact sets in asymmetric Efimov-Stechkin spaces and convexity of almost suns ⋮ Ball-complete sets and solar properties of sets in asymmetric spaces

Cites Work

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• Nonsmooth analysis
• Fréchet differentiability of the distance function and the structure of sets
• The differentiability of real functions on normed linear space using generalized subgradients
• Subdifferentiability and superdifferentiability of distance functions
• Essentially smooth Lipschitz functions
• Necessary conditions for differentiability of distance functions
• Approximate properties of sets in Banach spaces
• Almost convex and Chebyshev sets
• Connectedness and solarity in problems of best and near-best approximation
• A distance function property implying differentiability
• Differentiability of Distance Functions and a Proximinal Property Inducing Convexity
• Optimization and nonsmooth analysis
• Differentiation of Real-Valued Functions and Continuity of Metric Projections
• The Proximal Normal Formula in Banach Space
• Chebyshev Sets in C[0,1 Which are not Suns]
• An N-Parameter Chebyshev Set which is not a Sun
• Generalized subdifferential of the distance function

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