A generalization of an Ekeland-Lebourg theorem and the differentiability of distance functions
Zajíček, L.
Similarity:
Displaying similar documents to “On the Fréchet differentiability of distance functions”
A generalization of an Ekeland-Lebourg theorem and the differentiability of distance functions
The topological complexity of sets of convex differentiable functions.
Mohammed Yahdi (1998)
Revista Matemática Complutense
Similarity:
Let C(X) be the set of all convex and continuous functions on a separable infinite dimensional Banach space X, equipped with the topology of uniform convergence on bounded subsets of X. We show that the subset of all convex Fréchet-differentiable functions on X, and the subset of all (not necessarily equivalent) Fréchet-differentiable norms on X, reduce every coanalytic set, in particular they are not Borel-sets.
On differentiability of strongly α(·)-paraconvex functions in non-separable Asplund spaces
S. Rolewicz (2005)
Studia Mathematica
Similarity:
In Rolewicz (2002) it was proved that every strongly α(·)-paraconvex function defined on an open convex set in a separable Asplund space is Fréchet differentiable on a residual set. In this paper it is shown that the assumption of separability is not essential.
Separable reduction theorems by the method of elementary submodels
Marek Cúth (2012)
Fundamenta Mathematicae
Similarity:
We simplify the presentation of the method of elementary submodels and we show that it can be used to simplify proofs of existing separable reduction theorems and to obtain new ones. Given a nonseparable Banach space X and either a subset A ⊂ X or a function f defined on X, we are able for certain properties to produce a separable subspace of X which determines whether A or f has the property in question. Such results are proved for properties of sets: of being dense, nowhere dense,...
Remarks on Fréchet differentiability of pointwise Lipschitz, cone-monotone and quasiconvex functions
Luděk Zajíček (2014)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
We present some consequences of a deep result of J. Lindenstrauss and D. Preiss on -almost everywhere Fréchet differentiability of Lipschitz functions on (and similar Banach spaces). For example, in these spaces, every continuous real function is Fréchet differentiable at -almost every at which it is Gâteaux differentiable. Another interesting consequences say that both cone-monotone functions and continuous quasiconvex functions on these spaces are -almost everywhere Fréchet...