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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
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