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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
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