Search results for "Convex space"

showing 7 items of 27 documents

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
researchProduct

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
researchProduct

Banach spaces which are r-uniformly noncreasy

2003

Abstract We consider a family of spaces wider than UNC spaces introduced by Prus, and we give some fixed point results in the setting of these spaces.

Pure mathematicsApplied MathematicsMathematical analysisUniformly convex spaceBanach manifoldSpace (mathematics)Quantitative Biology::GenomicsFréchet spaceLocally convex topological vector spaceInterpolation spaceBirnbaum–Orlicz spaceLp spaceAnalysisMathematicsNonlinear Analysis: Theory, Methods & Applications
researchProduct

An overview on bounded elements in some partial algebraic structures

2015

The notion of bounded element is fundamental in the framework of the spectral theory. Before implanting a spectral theory in some algebraic or topological structure it is needed to establish which are its bounded elements. In this paper, we want to give an overview on bounded elements of some particular algebraic and topological structures, summarizing our most recent results on this matter.

Pure mathematicsEngineeringSpectral theorySettore MAT/05 - Analisi MatematicaAlgebraic structurebusiness.industryBounded functionStructure (category theory)Mechanical engineeringBounded elements (*-semisimple topological) partial *-algebras C*-inductive locally convex spacesAlgebraic numberElement (category theory)business
researchProduct

Constrained and unconstrained problems in location theory and inner products

1997

In a real normed space X the optimization problem associated to a finite subset and to a family of positive weights with the objective function [UM0001] has some well known properties when X is an ...

Strictly convex spaceEnergetic spaceMathematical optimizationInner product spaceControl and OptimizationOptimization problemSignal ProcessingApplied mathematicsLocation theoryAnalysisComputer Science ApplicationsNormed vector spaceMathematicsNumerical Functional Analysis and Optimization
researchProduct

Geometric mean and triangles inscribed in a semicircle in Banach spaces

2008

AbstractWe consider the triangles with vertices x, −x and y where x,y are points on the unit sphere of a normed space. Using the geometric means of the variable lengths of the sides of these triangles, we define two geometric constants for Banach spaces. These constants are closely related to the modulus of convexity of the space under consideration, and they seem to represent a useful tool to estimate the exact values of the James and Jordan–von Neumann constants of some Banach spaces.

Unit sphereUniformly non-square Banach spacePure mathematicsApplied MathematicsMathematical analysisBanach spaceUniformly convex spaceBanach manifoldModulus of convexitySpace (mathematics)Normal structureConvexityGeometry of normed spacesInterpolation spaceLp spaceAnalysisNormed vector spaceMathematicsJournal of Mathematical Analysis and Applications
researchProduct

Characterizations of convex approximate subdifferential calculus in Banach spaces

2016

International audience; We establish subdifferential calculus rules for the sum of convex functions defined on normed spaces. This is achieved by means of a condition relying on the continuity behaviour of the inf-convolution of their corresponding conjugates, with respect to any given topology intermediate between the norm and the weak* topologies on the dual space. Such a condition turns out to also be necessary in Banach spaces. These results extend both the classical formulas by Hiriart-Urruty and Phelps and by Thibault.

[ MATH ] Mathematics [math]Mathematics::Functional AnalysisApproximate subdifferentialDual spaceConvex functionsApplied MathematicsGeneral MathematicsBanach spaceUniformly convex spaceSubderivativeApproximate variational principleCalculus rulesLocally convex topological vector spaceCalculusInterpolation spaceMSC: Primary 49J53 52A41 46N10[MATH]Mathematics [math]Reflexive spaceLp spaceMathematics
researchProduct