Search results for "Set-valued Pettis"

showing 3 items of 3 documents

Henstock–Kurzweil–Pettis integrability of compact valued multifunctions with values in an arbitrary Banach space

2013

Abstract The aim of this paper is to describe Henstock–Kurzweil–Pettis (HKP) integrable compact valued multifunctions. Such characterizations are known in case of functions (see Di Piazza and Musial (2006)  [16] ). It is also known (see Di Piazza and Musial (2010)  [19] ) that each HKP-integrable compact valued multifunction can be represented as a sum of a Pettis integrable multifunction and of an HKP-integrable function. Invoking to that decomposition, we present a pure topological characterization of integrability. Having applied the above results, we obtain two convergence theorems, that generalize results known for HKP-integrable functions. We emphasize also the special role played in …

Discrete mathematicsMathematics::Functional AnalysisProperty (philosophy)Henstock integralIntegrable systemApplied MathematicsBanach spaceconvergence theoremsFunction (mathematics)Characterization (mathematics)set-valued Henstock-Kurzweil-Pettis integralset-valued Pettis integralsupport functionMultifunctionSettore MAT/05 - Analisi MatematicaConvergence (routing)AnalysisselectorMathematicsJournal of Mathematical Analysis and Applications
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Gauge integrals and selections of weakly compact valued multifunctions

2016

In the paper Henstock, McShane, Birkhoff and variationally multivalued integrals are studied for multifunctions taking values in the hyperspace of convex and weakly compact subsets of a general Banach space X. In particular the existence of selections integrable in the same sense of the corresponding multifunctions has been considered.

Pure mathematicsIntegrable systemSelection (relational algebra)Multifunction; Selection; Set-valued Pettis Henstock and McShane integrals; Analysis; Applied MathematicsSet-valued PettisBanach spaceMathematics::General Topology01 natural sciences28B20 26E25 26A39 28B05 46G10 54C60 54C65Settore MAT/05 - Analisi MatematicaFOS: Mathematics0101 mathematicsSelectionMathematicsMathematics::Functional AnalysisApplied Mathematics010102 general mathematicsMathematical analysisRegular polygonGauge (firearms)Functional Analysis (math.FA)Henstock and McShane integralsComputer Science::Other010101 applied mathematicsMathematics - Functional AnalysisHyperspaceMultifunctionAnalysisMultifunction set-valued Pettis Henstock and McShane integrals selection
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Some new results on integration for multifunction

2018

It has been proven in previous papers that each Henstock-Kurzweil-Pettis integrable multifunction with weakly compact values can be represented as a sum of one of its selections and a Pettis integrable multifunction. We prove here that if the initial multifunction is also Bochner measurable and has absolutely continuous variational measure of its integral, then it is a sum of a strongly measurable selection and of a variationally Henstock integrable multifunction that is also Birkhoff integrable.

Pure mathematicsSelection (relational algebra)Integrable systemApplied MathematicsGeneral Mathematics010102 general mathematicsMultifunction set-valued Pettis integral set-valued variationally Henstock and Birkhoff integrals selectionselectionAbsolute continuity01 natural sciencesMeasure (mathematics)Set-valued Pettis integralFunctional Analysis (math.FA)28B20 26E25 26A39 28B05 46G10 54C60 54C65Mathematics - Functional Analysisset-valued Pettis integral010101 applied mathematicsMultifunctionSettore MAT/05 - Analisi MatematicaHenstock and Birkhoff integralsFOS: Mathematicsset-valued variationally0101 mathematicsSet-valued variationally henstock and birkhoff integralMathematicsRicerche di Matematica
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