Properties of distance functions on convex surfaces and applications

Jan Rataj; Luděk Zajíček

Displaying similar documents to “Properties of distance functions on convex surfaces and applications”

On the differentiation of convex functions in finite and infinite dimensional spaces

Luděk Zajíček (1979)

Czechoslovak Mathematical Journal

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On the points of non-differentiability of convex functions

David Pavlica (2004)

Commentationes Mathematicae Universitatis Carolinae

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We characterize sets of non-differentiability points of convex functions on $ℝ^{n}$ . This completes (in $ℝ^{n}$ ) the result by Zajíček [2] which gives a characterization of the magnitude of these sets.

On inverses of $δ$ -convex mappings

Jakub Duda (2001)

Commentationes Mathematicae Universitatis Carolinae

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In the first part of this paper, we prove that in a sense the class of bi-Lipschitz $δ$ -convex mappings, whose inverses are locally $δ$ -convex, is stable under finite-dimensional $δ$ -convex perturbations. In the second part, we construct two $δ$ -convex mappings from $ℓ_{1}$ onto $ℓ_{1}$ , which are both bi-Lipschitz and their inverses are nowhere locally $δ$ -convex. The second mapping, whose construction is more complicated, has an invertible strict derivative at $0$ . These mappings show that for (locally) $δ$ -convex...

Displaying similar documents to “Properties of distance functions on convex surfaces and applications”

On the differentiation of convex functions in finite and infinite dimensional spaces

On the points of non-differentiability of convex functions

On inverses of δ -convex mappings

On inverses of $δ$ -convex mappings