## An example of a $$\mathcal C^{1,1}$$ function, which is not a d.c. function.(English)Zbl 1090.46012

Summary: Let $$X = \ell _p$$, $$p \in (2,+\infty )$$. We construct a function $$f: X \to {\mathbb R}$$ which has Lipschitz Fréchet derivative on $$X$$ but is not a d.c. function.

### MSC:

 46B20 Geometry and structure of normed linear spaces 26B25 Convexity of real functions of several variables, generalizations

### Keywords:

Lipschitz Fréchet derivative; d.c. functions
Full Text: