Generic Gateaux differentiability via smooth perturbations

Gateaux Differentiability for Functionals of Type Orlicz-lorentz

Let (Ω,A, μ) be a σ-finite nonatomic measure space and let Λw,φ be the Orlicz-Lorentz space. We study the Gateaux differentiability of the functional Ψw,φ(f) = ∞ ∫ 0 φ(f∗)w. More precisely we give an exact characterization of those points in the Orlicz-Lorentz space Λw,φ where the Gateaux derivative exists. This paper extends known results already on Lorent spaces, Lw,q , 1 < q <∞. The case q =...

Differentiability via Directional Derivatives

Let F be a continuous function from an open subset D of a separable Banach space X into a Banach space Y. We show that if there is a dense G8 subset A of D and a Gs subset H of X whose closure has nonempty interior, such that for each a E A and each x E H the directional derivative DxF(a) of F at a in the direction x exists, then F is Giteaux differentiable on a dense G8 subset of D. If X is re...

Differentiability, Convenient Spaces and Smooth Diffeologies

We review the basic definitions and properties concerning smooth structures, convenient spaces, diffeological spaces and tangent structures. The relation between the first two is described. A tangent structure is constructed for each pre-convenient space. This one is proved to be convenient if and only if the space and the tangent fibres

Generic G&eaux- Differentiability of Convex Functions on Small Sets

The theory of generic differentiability of convex functions on Banach spaces is by now a well-explored part of infinite-dimensional geometry. All the attempts to solve this kind of problem have in common, as a working hypothesis, one special feature of the finite-dimensional case. Namely, convex functions are always considered to be defined on convex sets with nonempty interior. But typically, ...

Generic Fr6chet -differentiability of Convex Functions on Small Sets