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On the points of non-differentiability of convex functions

David Pavlica — 2004

Commentationes Mathematicae Universitatis Carolinae

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.

A d.c. $C^{1}$ function need not be difference of convex $C^{1}$ functions

David Pavlica — 2005

Commentationes Mathematicae Universitatis Carolinae

In [2] a delta convex function on $ℝ^{2}$ is constructed which is strictly differentiable at $0$ 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 $C^{1} (ℝ^{2})$ 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.

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On the points of non-differentiability of convex functions

A d.c. C 1 function need not be difference of convex C 1 functions

A d.c. $C^{1}$ function need not be difference of convex $C^{1}$ functions