Search results for "Convex analysis"

showing 9 items of 29 documents

Strictly convex metric spaces with round balls and fixed points

2005

Convex hullConvex analysisStrictly convex spaceCombinatoricsInjective metric spaceMathematical analysisConvex setConvex bodyConvex combinationConvex metric spaceMathematicsBanach Center Publications
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An upper bound for nonlinear eigenvalues on convex domains by means of the isoperimetric deficit

2010

We prove an upper bound for the first Dirichlet eigenvalue of the p-Laplacian operator on convex domains. The result implies a sharp inequality where, for any convex set, the Faber-Krahn deficit is dominated by the isoperimetric deficit.

Convex hullConvex analysisp-Laplace operatorGeneral MathematicsMathematical analysisConvex setDirichlet eigenvalueSubderivativeMathematics::Spectral TheoryCombinatoricsupper boundsSettore MAT/05 - Analisi MatematicaConvex polytopeConvex combinationAbsolutely convex setIsoperimetric inequalityMathematics
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Some Questions of Heinrich on Ultrapowers of Locally Convex Spaces

1993

In this note we treat some open problems of Heinrich on ultrapowers of locally convex spaces. In section 1 we investigate the localization of bounded sets in the full ultrapower of a locally convex space, in particular the coincidence of the full and the bounded ultrapower, mainly concentrating in the case of (DF)-spaces. In section 2 we provide a partial answer to a question of Heinrich on commutativity of strict inductive limits and ultrapowers. In section 3 we analyze the relation between some natural candidates for the notion of superreflexivity in the setting of Frechet spaces. We give an example of a Frechet-Schwartz space which is not the projective limit of a sequence of superreflex…

Discrete mathematicsConvex analysisMathematics::Functional AnalysisPure mathematicsSequenceGeneral MathematicsBanach spaceConvex setUltraproductSpace (mathematics)Mathematics::LogicBounded functionLocally convex topological vector spaceMathematicsMathematische Nachrichten
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A differential equation approach to implicit sweeping processes

2019

International audience; In this paper, we study an implicit version of the sweeping process. Based on methods of convex analysis, we prove the equivalence of the implicit sweeping process with a differential equation, which enables us to show the existence and uniqueness of the solution to the implicit sweeping process in a very general framework. Moreover, this equivalence allows us to give a characterization of nonsmooth Lyapunov pairs and invariance for implicit sweeping processes. The results of the paper are illustrated with two applications to quasistatic evolution variational inequalities and electrical circuits.

Lyapunov functionDifferential equation01 natural scienceslaw.inventionsymbols.namesakeEvolution variational inequalitylawApplied mathematicsUniqueness0101 mathematicsEquivalence (formal languages)[MATH]Mathematics [math]MathematicsConvex analysisApplied Mathematics010102 general mathematicsNonsmooth Lyapunov pairs010101 applied mathematicsregularizationMSC: 49J40 47J20 47J22 34G25 58E35 37L45Electrical networkVariational inequalitysymbolsMoreau's sweeping processAnalysisQuasistatic process
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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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Envelopes of open sets and extending holomorphic functions on dual Banach spaces

2010

We investigate certain envelopes of open sets in dual Banach spaces which are related to extending holomorphic functions. We give a variety of examples of absolutely convex sets showing that the extension is in many cases not possible. We also establish connections to the study of iterated weak* sequential closures of convex sets in the dual of separable spaces.

Pure mathematicsAlgebra of holomorphic functionsConvex setBanach spaceOpen set46E5046B10Balanced setFOS: MathematicsAbsolutely convex setComplex Variables (math.CV)MathematicsConvex analysisDiscrete mathematicsMathematics - Complex VariablesApplied MathematicsFunctional Analysis (math.FA)46E50; 46B20; 46B10Mathematics - Functional Analysis46B20Absolutely convex setInterpolation spaceReflexive spaceAnalysisBoundedly regular setDual pair
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The norm of the characteristic function of a set in the John‐Nirenberg space of exponent p

2020

Set (abstract data type)Characteristic function (convex analysis)Pure mathematicsGeneral MathematicsGeneral EngineeringExponentSpace (mathematics)Nirenberg and Matthaei experimentBounded mean oscillationMathematicsMathematical Methods in the Applied Sciences
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An overview of semi-infinite programming theory and related topics through a generalization of the alternative theorems

1984

We propose new alternative theorems for convex infinite systems which constitute the generalization of the corresponding toGale, Farkas, Gordan andMotzkin. By means of these powerful results we establish new approaches to the Theory of Infinite Linear Inequality Systems, Perfect Duality, Semi-infinite Games and Optimality Theory for non-differentiable convex Semi-Infinite Programming Problem.

TheoryofComputation_MISCELLANEOUSStatistics and ProbabilityConvex analysisDiscrete mathematicsGeneralizationLinear matrix inequalityRegular polygonDuality (optimization)Optimality theorySemi-infinite programmingAlgebraLinear inequalityTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESStatistics Probability and UncertaintyMathematicsTrabajos de Estadistica y de Investigacion Operativa
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Convex analysis and dual problems

2018

Tässä tutkielmassa tarkastellaan valittujen variaatiolaskennan ongelmien ja näiden duaaliongelmien välisiä suhteita. Tutkielmassa esitetään aiheen yleinen teoria ja annetaan esimerkkejä sovelluksista.

convex analysiscalculus of variations
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