Fréchet differentiability of Lipschitz functions (a survey). (Q2760117)

This survey paper outlines rather recent and rather deep results on Fréchet differentiability of Lipschitz maps between separable Banach spaces. The following topics are covered. (1)~Results on Gâteaux differentiability; (2)~Examples and theorems showing the non-existence of Fréchet derivatives in certain cases; (3)~Existence results for \(\varepsilon\)-Fréchet derivatives; (4)~Existence results for Fréchet derivatives; (5)~Questions related to the mean value theorem for Fréchet derivatives. The final section contains a well commented list of open problems in this area.NEWLINENEWLINEFor more details, see the papers by \textit{W. B. Johnson}, \textit{J. Lindenstrauss}, \textit{D. Preiss} and \textit{G. Schechtman} [Proc. Lond. Math. Soc., III. Ser. 84, 711--746 (2002; Zbl 1023.46046)] and \textit{J. Lindenstrauss} and \textit{D. Preiss} [Ann. Math. (2) 157, 257--288 (2003; Zbl 1171.46313)].NEWLINENEWLINEFor the entire collection see [Zbl 0971.00063].