Search results for "Injective metric space"

showing 10 items of 70 documents

Slopes of Kantorovich potentials and existence of optimal transport maps in metric measure spaces

2014

We study optimal transportation with the quadratic cost function in geodesic metric spaces satisfying suitable non-branching assumptions. We introduce and study the notions of slope along curves and along geodesics and we apply the latter to prove suitable generalizations of Brenier's theorem of existence of optimal maps.

Mathematics - Differential GeometryPure mathematicsGeodesicApplied MathematicsInjective metric spacenon-brancingMathematical analysis49Q20 53C23Metric Geometry (math.MG)Measure (mathematics)geodesic metric spaceConvex metric spaceIntrinsic metricMetric spaceMathematics - Metric GeometryDifferential Geometry (math.DG)Metric (mathematics)FOS: Mathematicsupper gradientMetric mapoptimal transportationMathematics
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Representation of Quasi-Measure by Henstock–Kurzweil Type Integral on a Compact-Zero Dimensional Metric Space

2009

Abstract A derivation basis is introduced in a compact zero-dimensional metric space 𝑋. A Henstock–Kurzweil type integral with respect to this basis is defined and used to represent the so-called quasi-measure on 𝑋.

Metric spaceHenstock–Kurzweil integralGeneral MathematicsInjective metric spaceMathematical analysisMetric (mathematics)Measure (physics)Pseudometric spaceType (model theory)MathematicsConvex metric spacegmj
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Henstock type integral in compact zero-dimensional metric space and quasi-measures representations

2012

Properties of a Henstock type integral defined on a compact zero-dimensional metric space are studied. Theorems on integral representation of so-called quasi-measures, i.e., linear functionals on the space of “polynomials” defined on the space of the above mentioned type, are obtained.

Metric spaceIntegral representationSettore MAT/05 - Analisi MatematicaGeneral MathematicsInjective metric spaceMathematical analysisZero (complex analysis)Pseudometric spaceType (model theory)Space (mathematics)MathematicsHestock type integral quasi measure
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Graphical metric space: a generalized setting in fixed point theory

2016

Building on recent ideas of Jachymski, we work on the notion of graphical metric space and prove an analogous result for the contraction mapping principle. In particular, the triangular inequality is replaced by a weaker one, which is satisfied by only those points which are situated on some path included in the graphical structure associated with the space. Some consequences, examples and an application to integral equations are presented to confirm the significance and unifying power of obtained generalizations.

Pseudometric space01 natural sciencesGraphIntrinsic metricOrdered metric spaceSettore MAT/05 - Analisi MatematicaGraphical metric spaceContraction mapping0101 mathematicsMathematicsDiscrete mathematicsAlgebra and Number TheoryApplied MathematicsInjective metric space010102 general mathematicsFixed pointConvex metric space010101 applied mathematicsAlgebraComputational MathematicsMetric spaceGeometry and TopologySettore MAT/03 - GeometriaMetric differentialAnalysisFisher information metric
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Fixed points for Geraghty-Contractions in partial metric spaces

2015

We establish some fixed point theorems for mappings satisfying Geraghty-type contractive conditions in the setting of partial metric spaces and ordered partial metric spaces. Presented theorems extend and generalize many existing results in the literature. Examples are given showing that these results are proper extensions of the existing ones. c ©2014 All rights reserved.

Pure mathematicsAlgebra and Number TheoryInjective metric spaceEquivalence of metricsCoincidence point partial metric space ordered partial metric space Geraghty-type contractive condition fixed point.TopologyIntrinsic metricConvex metric spaceUniform continuityMetric spaceSettore MAT/05 - Analisi MatematicaFréchet spaceMetric mapAnalysisMathematicsJournal of Nonlinear Sciences and Applications
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Common fixed points for self mappings on compact metric spaces

2013

In this paper we obtain a result of existence of points of coincidence and of common fixed points for two self mappings on compact metric spaces satisfying a contractive condition of Suzuki type. We also present some examples to illustrate our results. Moreover, using the scalarization method of Du, we deduce a result of common fixed point in compact cone metric spaces.

Pure mathematicsApplied MathematicsInjective metric spaceFixed-point propertyTopologyIntrinsic metricConvex metric spaceComputational MathematicsUniform continuityMetric spaceRelatively compact subspaceSettore MAT/05 - Analisi MatematicaCompact metric spaces Common fixed points Suzuki fixed point theorem Scalarization Cone metric spacesMetric mapMathematicsApplied Mathematics and Computation
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Weakly controlled Moran constructions and iterated functions systems in metric spaces

2011

We study the Hausdorff measures of limit sets of weakly controlled Moran constructions in metric spaces. The separation of the construction pieces is closely related to the Hausdorff measure of the corresponding limit set. In particular, we investigate different separation conditions for semiconformal iterated function systems. Our work generalizes well known results on self-similar sets in metric spaces as well as results on controlled Moran constructions in Euclidean spaces.

Pure mathematicsClosed set28A8028A80 28A78 (Primary); 37C45 (Secondary)General MathematicsHausdorff dimensionDynamical Systems (math.DS)Hausdorff measureCombinatoricsopen set conditionsemikonforminen iteroitu funktiojärjestelmäsemiconformal iterated function systemFOS: Mathematics37C45 (Secondary)Hausdorff measureHausdorff-ulottuvuusMathematics - Dynamical SystemsHausdorffin mittaMathematicsball condition37C45avoimen joukon ehtoMoran-konstruktiofinite clustering propertyInjective metric spaceHausdorff spaceMoran constructionäärellinen pakkautuminenConvex metric space28A80 28A78 (Primary)Metric spaceHausdorff distance28A78palloehtoNormal space
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Common fixed points in cone metric spaces

2007

In this paper we consider a notion of g-weak contractive mappings in the setting of cone metric spaces and we give results of common fixed points. This results generalize some common fixed points results in metric spaces and some of the results of Huang and Zhang in cone metric spaces.

Pure mathematicsFixed point theoremGeneral MathematicsInjective metric spaceMathematical analysisComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISIONT-normb-metric spacesEquivalence of metricsConvex metric spaceIntrinsic metricUniform continuityMetric spaceMetric mapMetric spaceMathematicsRendiconti del Circolo Matematico di Palermo
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Weakly \varphi-pairs and common fixed points in cone metric spaces

2009

In this paper we introduce a weak contractive condition, called weakly \varphi-pair, for two mappings in the framework of cone metric spaces and we prove a theorem which ensures existence and uniqueness of common fixed points for such mappings. Also we obtain a result on points of coincidence. These results extend and generalize well-known comparable results in the literature.

Pure mathematicsGeneral MathematicsInjective metric spaceMathematical analysisCoincidence pointsFixed pointConvex metric spaceIntrinsic metricMetric spaceCommon fixed pointCone (topology)Settore MAT/05 - Analisi MatematicaWeakly \varphi-pairCone metric spaceUniquenessCoincidence pointMathematics
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Common fixed point results for three maps in G-metric spaces

2011

In this paper, we use the setting of generalized metric spaces to obtain common fixed point results for three maps. These results generalize several well known comparable results in the literature.

Pure mathematicsGeneral MathematicsInjective metric spaceProduct metricTopologyFixed-point propertyConvex metric spaceIntrinsic metricMetric spaceSchauder fixed point theoremSettore MAT/05 - Analisi MatematicaMetric mapCommon fixed point generalized metric spaceMathematicsFilomat
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