Displaying similar documents to “On a simultaneous selection theorem”

Continuous selection theorems

Michał Kisielewicz (2005)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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Continuous approximation selection theorems are given. Hence, in some special cases continuous versions of Fillipov's selection theorem follow.

On the extension and generation of set-valued mappings of bounded variation

V. V. Chistyakov, A. Rychlewicz (2002)

Studia Mathematica

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We study set-valued mappings of bounded variation of one real variable. First we prove the existence of an extension of a metric space valued mapping from a subset of the reals to the whole set of reals with preservation of properties of the initial mapping: total variation, Lipschitz constant or absolute continuity. Then we show that a set-valued mapping of bounded variation defined on an arbitrary subset of the reals admits a regular selection of bounded variation. We introduce a notion...

On a selection theorem of Blum and Swaminathan

Takamitsu Yamauchi (2004)

Commentationes Mathematicae Universitatis Carolinae

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Blum and Swaminathan [Pacific J. Math. 93 (1981), 251–260] introduced the notion of ℬ -fixedness for set-valued mappings, and characterized realcompactness by means of continuous selections for Tychonoff spaces of non-measurable cardinal. Using their method, we obtain another characterization of realcompactness, but without any cardinal assumption. We also characterize Dieudonné completeness and Lindelöf property in similar formulations.

Two theorems on the Scorza Dragoni property for multifunctions

Gabriele Bonanno (1989)

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

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We point out two theorems on the Scorza Dragoni property for multifunctions. As an application, in particular, we improve a Carathéodory selection theorem by A. Cellina [4], by removing a compactness assumption.

The multi-morphisms and their properties and applications

Mirosław Ślosarski (2015)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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In this paper a new class of multi-valued mappings (multi-morphisms) is defined as a version of a strongly admissible mapping, and its properties and applications are presented.

A generalized Pettis measurability criterion and integration of vector functions

I. Dobrakov, T. V. Panchapagesan (2004)

Studia Mathematica

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For Banach-space-valued functions, the concepts of 𝒫-measurability, λ-measurability and m-measurability are defined, where 𝒫 is a δ-ring of subsets of a nonvoid set T, λ is a σ-subadditive submeasure on σ(𝒫) and m is an operator-valued measure on 𝒫. Various characterizations are given for 𝒫-measurable (resp. λ-measurable, m-measurable) vector functions on T. Using them and other auxiliary results proved here, the basic theorems of [6] are rigorously established.

Differential inclusions and multivalued integrals

Kinga Cichoń, Mieczysław Cichoń, Bianca Satco (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper we consider the nonlocal (nonstandard) Cauchy problem for differential inclusions in Banach spaces x'(t) ∈ F(t,x(t)), x(0)=g(x), t ∈ [0,T] = I. Investigation over some multivalued integrals allow us to prove the existence of solutions for considered problem. We concentrate on the problems for which the assumptions are expressed in terms of the weak topology in a Banach space. We recall and improve earlier papers of this type. The paper is...

On Weak Compactness and Lower Closure Results for Pettis Integrable (Multi)Functions

Erik J. Balder, Anna Rita Sambucini (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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In [4, 5, 7] an abstract, versatile approach was given to sequential weak compactness and lower closure results for scalarly integrable functions and multifunctions. Its main tool is an abstract version of the Komlós theorem, which applies to scalarly integrable functions. Here it is shown that this same approach also applies to Pettis integrable multifunctions, because the abstract Komlós theorem can easily be extended so as to apply to generalized Pettis integrable functions. Some...

Two theorems on the Scorza Dragoni property for multifunctions

Gabriele Bonanno (1989)

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

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We point out two theorems on the Scorza Dragoni property for multifunctions. As an application, in particular, we improve a Carathéodory selection theorem by A. Cellina [4], by removing a compactness assumption.