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

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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

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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

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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

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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

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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

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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

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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.