Differentiability of the distance function and points of multi-valuedness of the metric projection in Banach space

DOI10.21136/cmj.1983.101878zbMath0527.41028OpenAlexW370903190MaRDI QIDQ3308523

Luděk Zajíček

Publication date: 1983

Full work available at URL: https://eudml.org/doc/13383

zbMATH Keywords

distance functionmetric projectionuniformly Gateaux differentiable normLipschitz hypersurfaces

Mathematics Subject Classification ID

Normed linear spaces and Banach spaces; Banach lattices (46B99) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Derivatives of functions in infinite-dimensional spaces (46G05)

Related Items

On the size of the set of points where the metric projection exists, The differentiability of real functions on normed linear space using generalized subgradients, Regularity of the distance function from arbitrary closed sets, An occupation time formula for semimartingales in \(\mathbb{R}^N\), The tangent cone, the dimension and the frontier of the medial axis, Convex analysis in normed spaces and metric projections onto convex bodies, A universal differentiability set in Banach spaces with separable dual, New results in the theory of multivalued mappings. I: Topological characteristics and solvability of operator relations, Differential properties of the Moreau envelope, On the Clarke subdifferential of the distance function of a closed set, Attainment and (sub)differentiability of the infimal convolution of a function and the square of the norm, Directional derivatives of Lipschitz functions, Generalized derivatives of distance functions and the existence of nearest points, Derivatives of generalized distance functions and existence of generalized nearest points

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