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Viene studiata la semicontinuità rispetto alla topologia di $L^{\infty}(\Omega;\mathbf{R}^{m})$ per alcuni funzionali del Calcolo delle Variazioni dipendenti da funzioni a valori vettoriali.

Singolarità di funzioni semiconcave ed applicazioni al controllo ottimo

Pietro Albano (2000)

Bollettino dell'Unione Matematica Italiana

Singular dynamics for semiconcave functions

Piermarco Cannarsa, Yifeng Yu (2009)

Journal of the European Mathematical Society

Singular points of order $k$ of Clarke regular and arbitrary functions

Luděk Zajíček (2012)

Commentationes Mathematicae Universitatis Carolinae

Let $X$ be a separable Banach space and $f$ a locally Lipschitz real function on $X$ . For $k \in ℕ$ , let $Σ_{k} (f)$ be the set of points $x \in X$ , at which the Clarke subdifferential $\partial^{C} f (x)$ is at least $k$ -dimensional. It is well-known that if $f$ is convex or semiconvex (semiconcave), then $Σ_{k} (f)$ can be covered by countably many Lipschitz surfaces of codimension $k$ . 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

Tiberiu Trif (1998)

Commentationes Mathematicae Universitatis Carolinae

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

Vlastimil Klíma, Ivan Netuka (1981)

Czechoslovak Mathematical Journal

Sobre la concavidad de t-normas y de funciones triangulares.

Núria Agell (1984)

Stochastica

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.

Wolfgang Sander (1983)

Monatshefte für Mathematik

Some inequalities for a class of generalized means.

Guan, Kaizhong (2004)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Some representations of midconvex set-valued functions.

K. Nikodem, F., Vercillo, S. Papalini (1997)

Aequationes mathematicae

Some results on stability and on characterization of K-convexity of set-valued functions

Tiziana Cardinali, Francesca Papalini (1993)

Annales Polonici Mathematici

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

Attouch, H., Riahi, H., Théra, M. (1996)

Serdica Mathematical Journal

∗ 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...

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Displaying 1 – 19 of 19

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 $L^{\infty}$ for polyconvex integrals