Relaxed strongly nonconvex functions.
Remarks on delta-convex functions
Remarks on WDC sets
We study WDC sets, which form a substantial generalization of sets with positive reach and still admit the definition of curvature measures. Main results concern WDC sets . We prove that, for such , the distance function is a “DC aura” for , which implies that each closed locally WDC set in is a WDC set. Another consequence is that compact WDC subsets of form a Borel subset of the space of all compact sets.
Schur geometric convexity for differences of means.
Schur-convexity for a class of symmetric functions and its applications.
Schur-convexity of the complete elementary symmetric function.
Segments of Exponential Series and Regularly Varying Sequences
Semicontinuity in for polyconvex integrals
Viene studiata la semicontinuità rispetto alla topologia di per alcuni funzionali del Calcolo delle Variazioni dipendenti da funzioni a valori vettoriali.
Singolarità di funzioni semiconcave ed applicazioni al controllo ottimo
Singular dynamics for semiconcave functions
Singular points of order of Clarke regular and arbitrary functions
Let be a separable Banach space and a locally Lipschitz real function on . For , let be the set of points , at which the Clarke subdifferential is at least -dimensional. It is well-known that if is convex or semiconvex (semiconcave), then can be covered by countably many Lipschitz surfaces of codimension . We show that this result holds even for each Clarke regular function (and so also for each approximately convex function). Motivated by a resent result of A.D. Ioffe, we prove...
Singularities and equicontinuity of certain families of set-valued mappings
In the present paper we establish an abstract principle of condensation of singularities for families consisting of set-valued mappings. By using it as a basic tool, the condensation of the singularities and the equicontinuity of certain families of generalized convex set-valued mappings are studied. In particular, a principle of condensation of the singularities of families of closed convex processes is derived. This principle immediately yields the uniform boundedness theorem stated in [1, Theorem...
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.
Some Functional Inequalities.
Some inequalities for a class of generalized means.
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.
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...
Stabilité de L'épi-convergence en Dimension Finie