Displaying similar documents to “Covering dimension and differential inclusions”

On the covering dimension of the fixed point set of certain multifunctions

Ornella Naselli Ricceri (1991)

Commentationes Mathematicae Universitatis Carolinae


We study the covering dimension of the fixed point set of lower semicontinuous multifunctions of which many values can be non-closed or non-convex. An application to variational inequalities is presented.

A generalization of the Schauder fixed point theorem via multivalued contractions

Paolo Cubiotti, Beatrice Di Bella (2001)

Commentationes Mathematicae Universitatis Carolinae


We establish a fixed point theorem for a continuous function f : X E , where E is a Banach space and X E . Our result, which involves multivalued contractions, contains the classical Schauder fixed point theorem as a special case. An application is presented.

Module-valued functors preserving the covering dimension

Jan Spěvák (2015)

Commentationes Mathematicae Universitatis Carolinae


We prove a general theorem about preservation of the covering dimension dim by certain covariant functors that implies, among others, the following concrete results. If G G is a pathwise connected...

On convex and *-concave multifunctions

Bożena Piątek (2005)

Annales Polonici Mathematici


A continuous multifunction F:[a,b] → clb(Y) is *-concave if and only if the inclusion 1 / ( t - s ) s t F ( x ) d x ( F ( s ) * + F ( t ) ) / 2 holds for every s,t ∈ [a,b], s < t.

CM-Selectors for pairs of oppositely semicontinuous multivalued maps with p -decomposable values

Hôǹg Thái Nguyêñ, Maciej Juniewicz, Jolanta Ziemińska (2001)

Studia Mathematica


We present a new continuous selection theorem, which unifies in some sense two well known selection theorems; namely we prove that if F is an H-upper semicontinuous multivalued map on a separable metric space X, G is a lower semicontinuous multivalued map on X, both F and G take nonconvex L p ( T , E ) -decomposable closed values, the measure space T with a σ-finite measure μ is nonatomic, 1 ≤ p < ∞, L p ( T , E ) is the Bochner-Lebesgue space of functions defined on T with values in a Banach space E, F(x)...

Some fixed point theorems for multifunctions with applications in game theory

Būi Cong Cuōng


IntroductionThe main result of this paper is concerned with the conditions which guarantee that a multifunction f : C 2 X defined on an arbitrary subset C of a topological vector space X admits a point x of C such that x∈f(x).First, we give some definitions and propositions which are associated with semicontinuous multifunctions (Part 1).Next, in Part 2, we present a global convergence criterion on variable dimension algorithms for finding an approximate solution of the equation x∈f(x), and...

Levi's forms of higher codimensional submanifolds

Andrea D&amp;#039;Agnolo, Giuseppe Zampieri (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni


Let X C n , let M be a C 2 hypersurface of X , S be a C 2 submanifold of M . Denote by L M the Levi form of M at z 0 S . In a previous paper [3] two numbers s ± S , p , p T ˙ S * X z 0 are defined; for S = M they are the numbers of positive and negative eigenvalues for L M . For S M , p S × M T ˙ * S X ) , we show here that s ± S , p are still the numbers of positive and negative eigenvalues for L M when restricted to T z 0 C S . Applications to the concentration in degree for microfunctions at the boundary are given.