On D.C. mappings and differences of convex operators

Libor Veselý; Luděk Zajíček

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...

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