Displaying similar documents to “On D.C. mappings and differences of convex operators”

On inverses of δ -convex mappings

Jakub Duda (2001)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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...

Delta-convex mappings between Banach spaces and applications

L. L. Veselý, L. Zajíček

Similarity:

We investigate delta-convex mappings between normed linear spaces. They provide a generalization of functions which are representable as a difference of two convex functions (labelled as 5-convex or d.c. functions) and are considered in many articles. We show that delta-convex mappings have many good differentiability properties of convex functions and the class of them is very stable. For example, the class of locally delta-convex mappings is closed under superpositions and (in some...