Smoothness of a typical convex function
Sobre la concavidad de t-normas y de funciones triangulares.
In this note we prove that the unique concave t-norm is Minimum and, among the class of triangular functions that have the family of unit step-functions as idempotent elements, the unique concave triangular function is piM.
Solution de la question 1570, proposée par M. Rouché
Solution to the gradient problem of C.E. Weil.
In this paper we give a complete answer to the famous gradient problem of C. E. Weil. On an open set G ⊂ R2 we construct a differentiable function f: G → R for which there exists an open set Ω1 ⊂ R2 such that ∇f(p) ∈ Ω1 for a p ∈ G but ∇f(q) ∉ Ω1 for almost every q ∈ G. This shows that the Denjoy-Clarkson property does not hold in higher dimensions.
Some applications of the matrix Haffian in connection with differentiable matrix functions of a central Wishart variate.
In this paper we revisit Haff's seminal work on the matrix Haffian as we proposed to call it. We review some results, and give new derivations. Use is made of the link between the matrix Haffian ∇F and the differential of the matrix function, dF.
Some factorizations of matrix functions in several variables
We establish some criteria for a nonsingular square matrix depending on several parameters to be represented in the form of a matrix product of factors which depend on the single parameters.
Some full descriptive characterizations of the Henstock-Kurzweil integral in the Euclidean space
Using generalized absolute continuity, we characterize additive interval functions which are indefinite Henstock-Kurzweil integrals in the Euclidean space.
Some Functional Inequalities.
Some inequalities for a class of generalized means.
Some inverse mapping theorems
Some properties of functions with bounded mean oscillation
Some properties of real functions of two variables and some consequences
Some remarks on almost continuous functions
Some representations of midconvex set-valued functions.
Some results on stability and on characterization of K-convexity of set-valued functions
We present a stability theorem of Ulam-Hyers type for K-convex set-valued functions, and prove that a set-valued function is K-convex if and only if it is K-midconvex and K-quasiconvex.
Some results on (-pre, )-continuous functions.
Some sufficient conditions for regular approximate differentiability
Some versions of limit and Dieudonné-type theorems with respect to filter convergence for (ℓ)-group-valued measures
Some limit and Dieudonné-type theorems in the setting of (ℓ)-groups with respect to filter convergence are proved, extending earlier results.
Somme Ponctuelle D'operateurs Maximaux Monotones Pointwise Sum of two Maximal Monotone Operators
∗ Cette recherche a été partiellement subventionnée, en ce qui concerne le premier et le dernier auteur, par la bourse OTAN CRG 960360 et pour le second auteur par l’Action Intégrée 95/0849 entre les universités de Marrakech, Rabat et Montpellier.The primary goal of this paper is to shed some light on the maximality of the pointwise sum of two maximal monotone operators. The interesting purpose is to extend some recent results of Attouch, Moudafi and Riahi on the graph-convergence of maximal monotone...
Sommes de carrés de fonctions dérivables
On montre que toute fonction positive de classe définie sur un intervalle de est somme de deux carrés de fonctions de classe . En dimension 2, toute fonction positive de classe est somme d’un nombre fini de carrés de fonctions de classe , pourvu que ses dérivées d’ordre 4 s’annulent aux points où et s’annulent.