Search results for " Gauge integral"

showing 3 items of 3 documents

Relations among Gauge and Pettis integrals for cwk(X)-valued multifunctions

2019

The aim of this paper is to study relationships among "gauge integrals" (Henstock, Mc Shane, Birkhoff) and Pettis integral of multifunctions whose values are weakly compact and convex subsets of a general Banach space, not necessarily separable. For this purpose we prove the existence of variationally Henstock integrable selections for variationally Henstock integrable multifunctions. Using this and other known results concerning the existence of selections integrable in the same sense as the corresponding multifunctions, we obtain three decomposition theorems. As applications of such decompositions, we deduce characterizations of Henstock and ${\mathcal H}$ integrable multifunctions, toget…

Pure mathematicsIntegrable systemMathematics::Classical Analysis and ODEsBanach spaceselection01 natural sciences28B20 26E25 26A39 28B05 46G10 54C60 54C65Separable spaceSettore MAT/05 - Analisi Matematicagauge integralFOS: Mathematics0101 mathematicsMathematicsPettis integralMathematics::Functional AnalysisMultifunction Gauge integral Decomposition theorem for multifunction Pettis integral SelectionApplied Mathematics010102 general mathematicsRegular polygonExtension (predicate logic)Gauge (firearms)Functional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsMultifunctionPettis integraldecomposition theorem for multifunctionAnnali di Matematica Pura ed Applicata (1923 -)
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Multifunctions determined by integrable functions

2019

Integral properties of multifunctions determined by vector valued functions are presented. Such multifunctions quite often serve as examples and counterexamples. In particular it can be observed that the properties of being integrable in the sense of Bochner, McShane or Birkhoff can be transferred to the generated multifunction while Henstock integrability does not guarantee it.

Pure mathematicsPositive multifunctionIntegrable systemApplied Mathematicsselection02 engineering and technologymultifunction determined by a functionTheoretical Computer ScienceFunctional Analysis (math.FA)28B20 26E25 26A39 28B05 46G10 54C60 54C65Mathematics - Functional AnalysisPositive multifunction gauge integral selection multifunction determined by a function measure theory.measure theorySettore MAT/05 - Analisi MatematicaArtificial Intelligence020204 information systemsgauge integral0202 electrical engineering electronic engineering information engineeringFOS: Mathematics020201 artificial intelligence & image processingVector-valued functionSoftwareCounterexampleMathematics
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Integration of multifunctions with closed convex values in arbitrary Banach spaces

2018

Integral properties of multifunctions with closed convex values are studied. In this more general framework not all the tools and the technique used for weakly compact convex valued multifunctions work. We pay particular attention to the "positive multifunctions". Among them an investigation of multifunctions determined by vector-valued functions is presented. Finally, decomposition results are obtained for scalarly and gauge-defined integrals of multifunctions and a full description of McShane integrability in terms of Henstock and Pettis integrability is given.

Mathematics::Functional AnalysisPositive multifunctionPhysics::Medical PhysicsMathematics::Optimization and ControlselectionPositive multifunction gauge integral decomposition theorem for multifunctionselection measure theoryComputer Science::OtherFunctional Analysis (math.FA)Mathematics - Functional Analysismeasure theorySettore MAT/05 - Analisi Matematicagauge integralFOS: Mathematicsdecomposition theorem for multifunction28B20 26E25 26A39 28B0 46G10 54C60 54C65
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