Search results for "Pettis Integral"

showing 10 items of 43 documents

On weakly measurable stochastic processes and absolutely summing operators

2006

A characterization of absolutely summing operators by means of McShane integrable stochastic processes is considered

Pettis integralSettore MAT/05 - Analisi MatematicaStochastic processGeneral MathematicsMathematical analysisApplied mathematicsPettis integral McShane integral amart uniform amart absolutely summing operatorsMathematicsMathematica Bohemica
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Radon–Nikodým Theorems for Finitely Additive Multimeasures

2015

In this paper we deal with interval multimeasures. We show some Radon–Nikodým theorems for such multimeasures using multivalued Henstock or Henstock–Kurzweil–Pettis derivatives. We do not use the separability assumption in the results.

Pure mathematicsHenstock–Kurzweil integralchemistrySettore MAT/05 - Analisi MatematicaApplied MathematicsMathematical analysischemistry.chemical_elementRadonMultifunction Henstock–Kurzweil integral Henstock–Kurzweil–Pettis integral selection Radon–Nikodým theoremAnalysisSelection (genetic algorithm)Mathematics
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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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Kurzweil-Henstock type integration on Banach spaces

2004

In this paper properties of Kurzweil-Henstock and Kurzweil-Henstock-Pettis integrals for vector-valued functions are studied. In particular, the absolute integrability for Kurzweil-Henstock integrable functions is characterized and a Kurzweil-Henstock version of the Vitali Theorem for Pettis integrable functions is given.

Pure mathematicsIntegrable systemequiintegrabilityInfinite-dimensional vector functionMathematical analysisBanach spaceRiemann–Stieltjes integralType (model theory)Infinite-dimensional holomorphyKurzweil-Henstock integral28B0526A39Pettis integralGeometry and TopologyDaniell integralLp spaceAnalysisMathematics
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Strongly measurable Kurzweil-Henstock type integrable functions and series

2008

We give necessary and sufficient conditions for the scalar Kurzweil-Henstock integrability and the Kurzweil-Henstock-Pettis integrability of functions $f:[1, infty) ightarrow X$ defined as $f=sum_{n=1}^infty x_n chi_{[n,n+1)}$. Also the variational Henstock integrability is considered

Pure mathematicsMathematics (miscellaneous)Integrable systemKurzweil-Henstock integral Kurzweil-Henstock-Pettis integral variational Henstock integralSettore MAT/05 - Analisi MatematicaMathematical analysisScalar (mathematics)Mathematics
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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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A variational henstock integral characterization of the radon-nikodým property

2009

A characterization of Banach spaces possessing the Radon-Nikodym property is given in terms of finitely additive interval functions. We prove that a Banach space X has the RNP if and only if each X-valued finitely additive interval function possessing absolutely continuous variational measure is a variational Henstock integral of an X-valued function. Due to that characterization several X-valued set functions that are only finitely additive can be represented as integrals.

Settore MAT/05 - Analisi MatematicaHenstock integral Pettis integral variational measure Radon-Nikodym property
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MR3093276 Reviewed Naralenkov, K. M. On continuity and compactness of some vector-valued integrals. Rocky Mountain J. Math. 43 (2013), no. 3, 1015–10…

2014

Settore MAT/05 - Analisi MatematicaHenstock-Kurzweil-Pettis integral
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ZBL MS 63/6 Satco, Bianca-Renata; Turcu, Corneliu-Octavian Henstock-Kurzweil-Pettis integral and weak topologies in nonlinear integral equations on t…

2013

The authors prove an existence result for a nonlinear integral equation on time scales under weak topology assumption in the target Banach space. In the setting of vector valued functions on time scales they consider the Henstock-Kurzweil-Pettis $\Delta$-integral which is a kind of Henstock integral recently introduced by Cichon, M. [Commun. Math. Anal. 11 (2011), no. 1, 94�110]. In this framework they show the existence of weakly continuous solutions for an integral equation x(t)= f(t, x(t))+ (HKP)\int_0^t g(t,s,x(s)) \Delta s governed by the sum of two operators: a continuous operator and an integral one. The main tool to get the solutions is a generalization of Krasnosel'skii fixed point…

Settore MAT/05 - Analisi MatematicaHenstock-Kurzweil-Pettis integraltime scalefixed point theoremnonlinear integral equation
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Decomposability in the space of HKP-integrable functions

2014

In this paper we introduce the notion of decomposability in the space of Henstock-Kurzweil-Pettis integrable (for short HKP-integrable) functions. We show representations theorems for decomposable sets of HKP-integrable or Henstock integrable functions, in terms of the family of selections of suitable multifunctions.

Settore MAT/05 - Analisi MatematicaMultifunction Henstock-Kurzweil integral Henstock-Kurzweil-Pettis integral decomposability
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