On Uniform Differentiability

On Pseudo-differentiability

We present some new relations between the pseudo-derivatives and parabolic epiderivatives recently introduced by Rockafellar, and also its infinite dimensional counterparts. Significant extensions of the most important known results are proven, which further clarify the range of applicability of this new theory.

On Concepts of Directional Differentiability

Various definitions of directional derivatives in topological vector spaces are compared. Directional derivatives in the sense of G~teaux, Fr6chet, and Hadamard are singled out from the general framework of cr-directional differentiability. It is pointed out that, in the case of finite-dimensional spaces and locally Lipschitz mappings, all these concepts of directional differentiability are equ...

On the Differentiability of Isometries

Let 9TC be an re-dimensional differentiable manifold of class Ck, k = l, • • • , oo, w (as usual O" means analytic, and we use the conventions * ±m= and w + w=w for integers m). An automorphism of 9TC is a one-to-one map of 911 onto itself which is of class C* and is nonsingular. Now let 9TC be given a Riemannian structure, i.e. a positive definite covariant tensor field of rank two, and su...

On Asymptotic Differentiability of Averages

Fréchet directional differentiability and Fréchet differentiability

Zaj́ıček has recently shown that for a lower semi-continuous real-valued function on an Asplund space, the set of points where the function is Fréchet subdifferentiable but not Fréchet differentiable is first category. We introduce another variant of Fréchet differentiability, called Fréchet directional differentiability, and show that for any realvalued function on a normed linear space, the se...