This is an announcement for the paper "Properties of Hadamard directional derivatives: Denjoy-Young-Saks theorem for functions on Banach spaces" by Ludek Zajicek.
Abstract: The classical Denjoy-Young-Saks theorem on Dini derivatives of arbitrary functions $f: \R \to \R$ was extended by U.S. Haslam-Jones (1932) and A.J. Ward (1935) to arbitrary functions on $\R^2$. This extension gives the strongest relation among upper and lower Hadamard directional derivatives $f^+_H (x,v)$, $f^-_H (x,v)$ ($v \in X$) which holds almost everywhere for an arbitrary function $f:\R^2\to \R$. Our main result extends the theorem of Haslam-Jones and Ward to functions on separable Banach spaces.
Archive classification: math.FA
Mathematics Subject Classification: Primary: 46G05, Secondary: 26B05
Submitted from: zajicek@karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1308.2415
or