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

Zelený, Miroslav

Commentat. Math. Univ. Carol. 43, No. 1, 149-154 (2002).

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