Search results for " McShane"

showing 10 items of 10 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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MR2886259 Naralenkov, Kirill Several comments on the Henstock-Kurzweil and McShane integrals of vector-valued functions. Czechoslovak Math. J. 61(136…

2012

In this paper the author essentially discusses the difference between the Henstock-Kurzweil and McShane integrals of vector-valued functions from the descriptive point of view. He first considers three notions of absolute continuity for vector-valued functions AC, AC*, AC_{\delta}) and studies the relationships between the corresponding classes of functions. Then he uses such notions to give descriptive characterizations of the Henstock-Kurzweil and McShane integrable functions.

Henstock-Kurzweil and McShane integralsSettore MAT/05 - Analisi Matematica
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Riemann type integrals for functions taking values in a locally convex space

2006

The McShane and Kurzweil-Henstock integrals for functions taking values in a locally convex space are defined and the relations with other integrals are studied. A characterization of locally convex spaces in which Henstock Lemma holds is given.

Convex analysisPure mathematicsGeneral MathematicsMathematical analysisMathematics::Classical Analysis and ODEsProper convex functionConvex setSubderivativeChoquet theoryLocally convex topological vector spaceConvex combinationPettis integral McShane integral Kurzweil-Henstock integral locally convex spacesAbsolutely convex setMathematicsCzechoslovak Mathematical Journal
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A Birkhoff type integral and the Bourgain property in a locally convex space

2007

An integral, called the $Bk$-integral, for functions taking values in a locally convex space is defined. Properties of $Bk$-integrable functions are considered and the relations with other integrals are studied. Moreover the $Bk$-integrability of bounded functions is compared with the Bourgain property.

Pettis integralMcShane integralPure mathematicsMathematical analysisConvex setlocally convex spaceRiemann–Stieltjes integralRiemann integralSingular integral28B05symbols.namesakePettis integral McShane integral Birkho integral locally convex spacesBounded functionPettis integralsymbolsPaley–Wiener integralGeometry and TopologyDaniell integralAnalysisBirkhoff integral46G10Mathematics
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Relations among Henstock, McShane and Pettis integrals for multifunctions with compact convex values

2013

Fremlin (Ill J Math 38:471–479, 1994) proved that a Banach space valued function is McShane integrable if and only if it is Henstock and Pettis integrable. In this paper we prove that the result remains valid also in case of multifunctions with compact convex values being subsets of an arbitrary Banach space (see Theorem 3.4). Di Piazza and Musial (Monatsh Math 148:119–126, 2006) proved that if \(X\) is a separable Banach space, then each Henstock integrable multifunction which takes as its values convex compact subsets of \(X\) is a sum of a McShane integrable multifunction and a Henstock integrable function. Here we show that such a decomposition is true also in case of an arbitrary Banac…

Pettis integralDiscrete mathematicsMathematics::Functional AnalysisPure mathematicsIntegrable systemGeneral MathematicsMultifunction McShane integral Henstock integral Pettis integral Henstock--Kurzweil--Pettis integral selectionMathematics::Classical Analysis and ODEsBanach spaceRegular polygonFunction (mathematics)Separable spaceSettore MAT/05 - Analisi MatematicaLocally integrable functionMathematicsMonatshefte für Mathematik
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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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A first return examination of vector valued integrals.

2009

We prove that for each Bochner integrable function f there exists a trajectory yielding the Bochner integral of f, and that on infinite dimensional Banach spaces there exist Pettis integrable functions f such that no trajectory yields the Pettis integral of f.

Trajectory first return integral Bochner integral Pettis integral McShane integral.Settore MAT/05 - Analisi Matematica
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A Decomposition Theorem for the Fuzzy Henstock Integral

2012

We study the fuzzy Henstock and the fuzzy McShane integrals for fuzzy-number valued functions. The main purpose of this paper is to establish the following decomposition theorem: a fuzzy-number valued function is fuzzy Henstock integrable if and only if it can be represented as a sum of a fuzzy McShane integrable fuzzy-number valued function and of a fuzzy Henstock integrable fuzzy number valued function generated by a Henstock integrable function.

Discrete mathematicsPure mathematicsIntegrable systemMathematics::General MathematicsLogicMathematics::Classical Analysis and ODEsFunction (mathematics)Fuzzy logicComputingMethodologies_PATTERNRECOGNITIONArtificial IntelligenceIf and only ifSettore MAT/05 - Analisi MatematicaFuzzy Henstock integral fuzzy McShane integral Henstock-Kurzweil and McShane equiintegrabilityFuzzy numberLocally integrable functionComputingMethodologies_GENERALMathematicsDecomposition theorem
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On the integration of Riemann-measurable vector-valued functions

2016

We confine our attention to convergence theorems and descriptive relationships within some subclasses of Riemann-measurable vector-valued functions that are based on the various generalizations of the Riemann definition of an integral.

Dominated convergence theoremRiemann-measurable functionPure mathematicsMeasurable functionGeneral Mathematics02 engineering and technologyLebesgue measurable gaugeLebesgue integration01 natural sciencessymbols.namesakeConvergence (routing)0202 electrical engineering electronic engineering information engineeringCalculusMathematics (all)0101 mathematicsMathematicsBirkhoff McShane Henstock and Pettis integralMathematics::Complex Variables010102 general mathematicsRiemann integralRiemann hypothesisBounded variationBounded variationAlmost uniform convergencesymbols020201 artificial intelligence & image processingVector-valued function$$ACG_*$$ACG∗and $$ACG_delta ^*$$ACGδ∗functionMonatshefte für Mathematik
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The Variational Mcshane Integral in Locally Convex Spaces

2009

The variational McShane integral for functions taking values in a locally convex space is defined, and it is characterized by means of the p-variation of the indefinite Pettis integral

Pettis integralConvex analysisMcShane integralPure mathematicsPettis integral McShane integral variational McShane integral locally convex spacesGeneral MathematicsMathematical analysisvariational McShane integral28B05Settore MAT/05 - Analisi Matematicalocally convex spacesLocally convex topological vector spacePettis integral46G10MathematicsRocky Mountain Journal of Mathematics
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