Gâteaux and Hadamard differentiability via directional differentiability
The author inspects the Gâteaux and Hadamard differentiablity as implied by directional differentiablity. The Ioffe result on the Hadamard differentiability is improved and generalized for vector-valued functions; cf. [\textit{A. Ioffe}, J. Convex Anal. 17, No. 3--4, 1019--1032 (2010; Zbl 1208.46043)].NEWLINENEWLINEAn analogous result on the connection between directional and Gâteaux derivatives is established, which generalizes a previous joint result by \textit{D. Preiss} and the author; see [Isr. J. Math. 125, 1--27 (2001; Zbl 1022.46026)].
scientific article; zbMATH DE number 6353706