An example of a function, which is not a d.c. function
Miroslav Zelený (2002)
Commentationes Mathematicae Universitatis Carolinae
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Let , . We construct a function which has Lipschitz Fréchet derivative on but is not a d.c. function.
Displaying similar documents to “A note on propagation of singularities of semiconcave functions of two variables”
An example of a function, which is not a d.c. function
Singular points of order of Clarke regular and arbitrary functions
Luděk Zajíček (2012)
Commentationes Mathematicae Universitatis Carolinae
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Let be a separable Banach space and a locally Lipschitz real function on . For , let be the set of points , at which the Clarke subdifferential is at least -dimensional. It is well-known that if is convex or semiconvex (semiconcave), then can be covered by countably many Lipschitz surfaces of codimension . We show that this result holds even for each Clarke regular function (and so also for each approximately convex function). Motivated by a resent result of A.D. Ioffe,...
On inverses of -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 -convex mappings, whose inverses are locally -convex, is stable under finite-dimensional -convex perturbations. In the second part, we construct two -convex mappings from onto , which are both bi-Lipschitz and their inverses are nowhere locally -convex. The second mapping, whose construction is more complicated, has an invertible strict derivative at . These mappings show that for (locally) -convex...
A d.c. function need not be difference of convex functions
David Pavlica (2005)
Commentationes Mathematicae Universitatis Carolinae
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In [2] a delta convex function on is constructed which is strictly differentiable at but it is not representable as a difference of two convex function of this property. We improve this result by constructing a delta convex function of class which cannot be represented as a difference of two convex functions differentiable at 0. Further we give an example of a delta convex function differentiable everywhere which is not strictly differentiable at 0.