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Article

Zelený, Miroslav
An example of a $\Cal C^{1,1}$ function, which is not a d.c. function. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 43 (2002), issue 1, pp. 149-154
MSC: 26B25, 46B20, 46G05 | MR 1903313 | Zbl 1090.46012
Keywords:
Lipschitz Fréchet derivative; d.c. functions
Summary:
Let $X = \ell_p$, $p \in (2,+\infty)$. We construct a function $f:X \to \Bbb R$ which has Lipschitz Fréchet derivative on $X$ but is not a d.c. function.
References:
[DGZ] Deville R., Godefroy G., Zizler V.: Smoothness and Renormings in Banach Spaces. Longman (1993). MR 1211634 | Zbl 0782.46019
[DVZ] Duda J., Veselý L., Zajíček L.: On d.c. functions and mappings. submitted to Atti Sem. Mat. Fis. Univ. Modena.
[VZ] Veselý L., Zajíček L.: Delta-convex mappings between Banach spaces and applications. Dissertationes Math. (Rozprawy mat.) 289 (1989), 52 pp. MR 1016045
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