Search results for "Set-valued"

showing 10 items of 20 documents

On Spaces of Bochner and Pettis Integrable Functions and Their Set-Valued Counterparts

2011

The aim of this paper is to give a brief summary of the Pettis and Bochner integrals, how they are related, how they are generalized to the set-valued setting and the canonical Banach spaces of bounded maps between Banach spaces that they generate. The main tool that we use to relate the Banach space-valued case to the set-valued case, is the R ̊adstr ̈om embedding theorem.

Pettis integralSet (abstract data type)Mathematics::Functional AnalysisPure mathematicsIntegrable systemBounded functionBanach latticeBochner integralBanach spaceEmbeddingAbsolutely summing operator Banach lattice Bochner integral Pettis integral cone absolutely summing operator integrably bounded set- valued function set-valued operator.Mathematics
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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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A decomposition of Denjoy-Khintchine-Pettis and Henstock-Kurzweil-Pettis integrable multifunctions

2010

We proved in one of our earlier papers that in case of separable Banach space valued multifunctions each Henstock-Kurzweil-Pettis integrable multifunction can be represented as a sum of one of its Henstock-Kurzweil-Pettis integrable selector and a Pettis integrable multifunction. Now, we prove that the same result can be achieved in case of an arbitrary Banach space. Moreover we show that an analogous result holds true also for the Denjoy-Khintchine-Pettis integrable multifunctions. Applying the representation theorem we describe the multipliers of HKP and DKP integrable functions. Then we use this description to obtain an operator characterization of HKP and DKP integrability.

Settore MAT/05 - Analisi MatematicaMultifunctions Pettis set-valued integral Kurzweil-Henstock integral Kurzweil-Henstock-Pettis integral support function Denjoy-Khintchine-Pettis integral selectors.
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Attractors for non-autonomous retarded lattice dynamical systems

2015

AbstractIn this paperwe study a non-autonomous lattice dynamical system with delay. Under rather general growth and dissipative conditions on the nonlinear term,we define a non-autonomous dynamical system and prove the existence of a pullback attractor for such system as well. Both multivalued and single-valued cases are considered.

Statistics and ProbabilityDifferential equations with delayDynamical systems theoryNon-autonomous systemslattice dynamical systemsPullback attractorHamiltonian systemLinear dynamical systemProjected dynamical systemAttractorQA1-939pullback attractorMathematicsNumerical AnalysisApplied MathematicsMathematical analysisdifferential equations with delaynon-autonomous systemsClassical mechanicsLattice dynamical systemsPullback attractorset-valued dynamical systemsSet-valued dynamical systemsLimit setRandom dynamical systemMathematicsAnalysis
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Juggler's exclusion process

2012

Juggler's exclusion process describes a system of particles on the positive integers where particles drift down to zero at unit speed. After a particle hits zero, it jumps into a randomly chosen unoccupied site. We model the system as a set-valued Markov process and show that the process is ergodic if the family of jump height distributions is uniformly integrable. In a special case where the particles jump according to a set-avoiding memoryless distribution, the process reaches its equilibrium in finite nonrandom time, and the equilibrium distribution can be represented as a Gibbs measure conforming to a linear gravitational potential.

Statistics and Probabilityset-valued Markov processmaximum entropy60K35 82C41General Mathematics82C41FOS: Physical sciencesMarkov process01 natural sciencespositive recurrencesymbols.namesakeGravitational potentialMarkov renewal process0103 physical sciencesjuggling patternFOS: MathematicsErgodic theory0101 mathematicsGibbs measureMathematical PhysicsMathematicsDiscrete mathematicsnoncolliding random walkProbability (math.PR)ta111010102 general mathematicsErgodicityMathematical analysisExclusion processMathematical Physics (math-ph)Gibbs measureDistribution (mathematics)set-avoiding memoryless distribution60K35Jumpsymbolsergodicity010307 mathematical physicsStatistics Probability and UncertaintyMathematics - Probability
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Random attractors for stochastic lattice systems with non-Lipschitz non-linearity

2012

In this paper we study the asymptotic behaviour of solutions of a first-order stochastic lattice dynamical system with an additive noise. We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions, so that uniqueness of the Cauchy problem fails to be true. Using the theory of multi-valued random dynamical systems we prove the existence of a random compact global attractor.

Stochastic lattice dynamical systemsrandom attractorset-valued dynamical system
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Fixed point theorems for α-set-valued quasi-contractions in b-metric spaces

2015

Recently, Samet et al. [B. Samet, C. Vetro and P. Vetro, Fixed point theorems for alpha-psi-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165] introduced the notion of alpha-psi-contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notions of alpha-set-valued contraction and alpha-set-valued quasi-contraction and we give some fixed point theorems for such classes of mappings in the setting of b-metric spaces and ordered b-metric spaces. The presented theorems extend, unify and generalize several well-known comparable results in the existing literature.

b-metric spaceordered b-metric spacesfixed pointSettore MAT/05 - Analisi Matematicaalpha-set-valued contractionalpha-set-valued quasi-contraction
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Convergence Analysis of Distributed Set-Valued Information Systems

2016

This paper focuses on the convergence of information in distributed systems of agents communicating over a network. The information on which the convergence is sought is not rep- resented by real numbers, as often in the literature, rather by sets. The dynamics of the evolution of information across the net- work is accordingly described by set-valued iterative maps. While the study of convergence of set-valued iterative maps is highly complex in general, this paper focuses on Boolean maps, which are comprised of arbitrary combinations of unions, intersections, and complements of sets. For these important class of systems, we provide tools to study both global and local convergence. A distr…

boolean dynamic systems0209 industrial biotechnologyClass (set theory)Geographic information systemTheoretical computer scienceBinary encoding boolean dynamic systems con- sensus algorithms convergence cooperative systems distributed information systems set-valued dynamic maps.consensus algorithms02 engineering and technologyBoolean algebraSet (abstract data type)symbols.namesakecooperative systems020901 industrial engineering & automationSettore ING-INF/04 - AutomaticaConvergence (routing)0202 electrical engineering electronic engineering information engineeringInformation systemElectrical and Electronic EngineeringMathematicsReal numberconvergencebusiness.industryset-valued dynamic mapsComputer Science Applications1707 Computer Vision and Pattern Recognitiondistributed information systemsComputer Science ApplicationsLocal convergenceControl and Systems EngineeringsymbolsBinary encoding; boolean dynamic systems; consensus algorithms; convergence; cooperative systems; distributed information systems; set-valued dynamic maps; Electrical and Electronic Engineering; Control and Systems Engineering; Computer Science Applications1707 Computer Vision and Pattern RecognitionBinary encoding020201 artificial intelligence & image processingbusinessIEEE Transactions on Automatic Control
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MR2407444 (2009e:60101) Labuschagne, Coenraad C. A. Join-semilattices of integrable set-valued martingales. Thai J. Math. 5 (2007), no. 1, 53--69. (R…

2009

Join-semilattices of integrable set-valued martingales

set-valued martingales
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