Search results for "Injective metric space"

showing 10 items of 70 documents

A Structural Theorem for Metric Space Valued Mappings of Φ-bounded Variation

2009

In this paper we introduce the notion of $\Phi$-bounded variation for metric space valued mappings defined on a subset of the real line. Such a notion generalizes the one for real functions introduced by M. Schramm, and many previous generalized variations. We prove a structural theorem for mappings of $\Phi$-bounded variation. As an application we show that each mapping of $\Phi$-bounded variation defined on a subset of $\mathbb{R}$ possesses a $\Phi$-variation preserving extension to the whole real line.

Discrete mathematicsInjective metric spaceextensionstructural theoremTotally bounded space54C35$\Phi$-bounded variation54E35Intrinsic metricmetric space valued mapings variation $Phi$-variation extension structural theorem.metric space valued mappingsUniform normSettore MAT/05 - Analisi MatematicaBounded functionBounded variationGeometry and Topologyvariation26A45Metric differentialReal lineAnalysisMathematics
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A Suzuki type fixed point theorem for a generalized multivalued mapping on partial Hausdorff metric spaces

2013

Abstract In this paper, we obtain a Suzuki type fixed point theorem for a generalized multivalued mapping on a partial Hausdorff metric space. As a consequence of the presented results, we discuss the existence and uniqueness of the bounded solution of a functional equation arising in dynamic programming.

Discrete mathematicsInjective metric spacepartial metric spaceFixed-point theoremFixed-point propertyCommon fixed pointSchauder fixed point theoremHausdorff distanceSettore MAT/05 - Analisi Matematicamulti-valued mappingContraction mappingGeometry and TopologyBrouwer fixed-point theoremKakutani fixed-point theoremMathematicsTopology and its Applications
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Metric or partial metric spaces endowed with a finite number of graphs: a tool to obtain fixed point results

2014

Abstract We give some fixed point theorems in the setting of metric spaces or partial metric spaces endowed with a finite number of graphs. The presented results extend and improve several well-known results in the literature. In particular, we discuss a Caristi type fixed point theorem in the setting of partial metric spaces, which has a close relation to Ekelandʼs principle.

Discrete mathematicsMetric spaceUniform continuityInjective metric spaceCaristi's fixed point theorem Ekeland's principle graph metric space partial metric space.Metric mapMetric treeGeometry and TopologyEquivalence of metricsSettore MAT/03 - GeometriaConvex metric spaceMathematicsIntrinsic metric
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Partial Hausdorff metric and Nadler’s fixed point theorem on partial metric spaces

2012

Abstract In this paper, we introduce the concept of a partial Hausdorff metric. We initiate study of fixed point theory for multi-valued mappings on partial metric space using the partial Hausdorff metric and prove an analogous to the well-known Nadlerʼs fixed point theorem. Moreover, we give a homotopy result as application of our main result.

Discrete mathematicsNadlerʼs fixed point theoremPure mathematicsInjective metric spacePartial Hausdorff metricMulti-valued mappingsNadler’s fixed point theoremMulti-valued mappingConvex metric spaceIntrinsic metricMetric spaceHausdorff distanceSettore MAT/05 - Analisi MatematicaHausdorff dimensionHausdorff measureGeometry and TopologyMetric differentialMathematics
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Fixed points and completeness on partial metric spaces

2015

Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a selfmapping on a partial metric space that characterizes the partial metric 0-completeness. In this paper we prove a fixed point result for a new class of…

Discrete mathematicsNumerical AnalysisPartial metric 0-completeneControl and OptimizationAlgebra and Number TheoryPartial metric spaceInjective metric spaceOrdered partial metric spaceEquivalence of metricsConvex metric spaceIntrinsic metricMetric spaceSettore MAT/05 - Analisi MatematicaSuzuki fixed point theoremCompleteness (order theory)Metric (mathematics)Discrete Mathematics and CombinatoricsMetric mapFixed and common fixed pointAnalysisMathematicsMiskolc Mathematical Notes
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Berinde mappings in orbitally complete metric spaces

2011

Abstract We give a fixed point theorem for a self-mapping satisfying a general contractive condition of integral type in orbitally complete metric spaces. Some examples are given to illustrate our obtained result.

Discrete mathematicsOrbitally complete metric space.General MathematicsApplied MathematicsInjective metric spaceGeneral Physics and AstronomyFixed-point theoremStatistical and Nonlinear PhysicsFixed pointGeneral contractive conditionIntrinsic metricConvex metric spaceMetric spaceFréchet spaceSettore MAT/05 - Analisi MatematicaMetric (mathematics)Metric differentialMathematics
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Common fixed points of generalized contractions on partial metric spaces and an application

2011

Abstract In this paper, common fixed point theorems for four mappings satisfying a generalized nonlinear contraction type condition on partial metric spaces are proved. Presented theorems extend the very recent results of I. Altun, F. Sola and H. Simsek [Generalized contractions on partial metric spaces, Topology and its applications 157 (18) (2010) 2778–2785]. As application, some homotopy results for operators on a set endowed with a partial metric are given.

Discrete mathematicsPartial metric spaceHomotopy.Applied MathematicsInjective metric space010102 general mathematicsEquivalence of metricsCommon fixed point01 natural sciencesCoincidence pointConvex metric spaceIntrinsic metric010101 applied mathematicsComputational MathematicsMetric spaceSettore MAT/05 - Analisi MatematicaMetric (mathematics)Metric mapWeakly compatible pair of mapping0101 mathematicsMetric differentialMathematicsApplied Mathematics and Computation
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Suzukiʼs type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces

2012

Abstract Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008) 1861–1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. In this paper we prove an analogous fixed point result for a self-mapping on a partial metric space or on a partially ordered metric space. Our results on partially ordered metric spaces generalize and extend some recent results of Ran and Reurings [A.C.M. Ran, M.C. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004…

Discrete mathematicsPartial metric spacesPartially ordered metric spacesInjective metric spaceMathematics::General TopologyPartial metric completenessEquivalence of metricsFixed-point propertyFixed points Common fixed points Partial metric spaces Partially ordered metric spaces Partial metric completenessConvex metric spaceIntrinsic metricLeast fixed pointFixed pointsMetric spaceSettore MAT/05 - Analisi MatematicaCommon fixed pointsGeometry and TopologyMetric differentialMathematicsTopology and its Applications
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Multi-valued $$F$$ F -contractions in 0-complete partial metric spaces with application to Volterra type integral equation

2013

We study the existence of fixed points for multi-valued mappings that satisfy certain generalized contractive conditions in the setting of 0-complete partial metric spaces. We apply our results to the solution of a Volterra type integral equation in ordered 0-complete partial metric spaces.

Discrete mathematicsPure mathematicsAlgebra and Number Theory0-completenepartial metric spacesApplied MathematicsInjective metric spaceclosed multi-valued mappingT-normEquivalence of metricsIntrinsic metricConvex metric spaceComputational MathematicsUniform continuityMetric spacefixed pointSettore MAT/05 - Analisi MatematicaFréchet spaceGeometry and TopologyF-contractionAnalysisMathematicsRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
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Existence of a common fixed point for a family of mappings of non‐expansive type on a metric space

1992

Existence of a common fixed point for a family of mappings of non‐expansive type on a metric space with a closure operator is proved.

Discrete mathematicsPure mathematicsApplied MathematicsInjective metric spacePseudometric spaceFixed-point propertyEducationConvex metric spaceIntrinsic metricMetric spaceMathematics (miscellaneous)Coincidence pointMetric differentialMathematicsInternational Journal of Mathematical Education in Science and Technology
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