Calcul différentiel généralisé
Categorical differential calculus for infinite dimensional spaces
Concerning a geometrical characterization of Fréchet differentiability
Continuity and Fréchet-Differentiability of Nemytskij Operators in Hölder Spaces.
Definition und grundlegende Eigenschaften des nichtlinearen adjungierten Operators
Dense Subdifferentiability and Trustworthiness for Arbitrary Subdifferentials
2000 Mathematics Subject Classification: 49J52, 49J50, 58C20, 26B09.We show that the properties of dense subdifferentiability and of trustworthiness are equivalent for any subdifferential satisfying a small set of natural axioms. The proof relies on a remarkable property of the subdifferential of the inf-convolution of two (non necessarily convex) functions. We also show the equivalence of the dense subdifferentiability property with other basic properties of subdifferentials such as a weak* Lipschitz...
Differentiability points of a distance function
Differentiable manifolds with generalized boundary
Differentiation in Normed Spaces
In this article we formalized the Fréchet differentiation. It is defined as a generalization of the differentiation of a real-valued function of a single real variable to more general functions whose domain and range are subsets of normed spaces [14].
Differentiation of measures.
Differenziabilità delle funzioni convesse a valori in spazi di successioni
Epi-differentiability and optimality conditions for an extremal problem under inclusion constraints.
Evaluation of Clarke's generalized gradient in optimization of variational inequalities
Flache Konvexität von Orliczräumen
Flett's mean value theorem in topological vector spaces.
Fréchet differentiability, strict differentiability and subdifferentiability
Fréchet directional differentiability and Fréchet differentiability
Zaj’ıček 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 real-valued function on a normed linear space, the set of points where the function is Fréchet directionally differentiable but not Fréchet differentiable...
Functions of class Ck without derivatives.
We describe a general axiomatic way to define functions of class Ck, k ∈ N∪{∞} on topological abelian groups. In the category of Banach spaces, this definition coincides with the usual one. The advantage of this axiomatic approach is that one can dispense with the notion of norms and limit procedures. The disadvantage is that one looses the derivative, which is replaced by a local linearizing factor. As an application we use this approach to define C∞ functions in the setting of graded/super manifolds....
Generalization of the formula of Faa di Bruno for a composite function with a vector argument.
Generalized gradients for locally Lipschitz integral functionals on non--type spaces of measurable functions
Let (Ω,μ) be a measure space, E be an arbitrary separable Banach space, be the dual equipped with the weak* topology, and g:Ω × E → ℝ be a Carathéodory function which is Lipschitz continuous on each ball of E for almost all s ∈ Ω. Put . Consider the integral functional G defined on some non--type Banach space X of measurable functions x: Ω → E. We present several general theorems on sufficient conditions under which any element γ ∈ X* of Clarke’s generalized gradient (multivalued C-subgradient)...