Search results for "multi-valued mapping"

showing 7 items of 7 documents

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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Some fixed point results for multi-valued mappings in partial metric spaces

2013

Abstract In this paper, we obtain some fixed point results for multi-valued mappings in partial metric spaces. Our results unify, generalize and complement various known comparable results from the current literature. An example is also included to illustrate the main result in the paper. MSC:46S40, 47H10, 54H25.

Discrete mathematicsPure mathematicscompleteness.Injective metric spaceApplied MathematicsIntrinsic metricConvex metric spaceMetric spacefixed pointSettore MAT/05 - Analisi Matematicamulti-valued mappingMetric (mathematics)partial Hausdorff metricMetric mapGeometry and TopologyMetric differentialCoincidence pointMathematics
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Fixed point and homotopy results for mixed multi-valued mappings in 0-complete partial metric spaces*

2015

We give sufficient conditions for the existence of common fixed points for a pair of mixed multi-valued mappings in the setting of 0-complete partial metric spaces. An example is given to demonstrate the usefulness of our results over the existing results in metric spaces. Finally, we prove a homotopy theorem via fixed point results.

Discrete mathematicsHomotopy categoryPartial metric spacefixed pointsApplied MathematicsInjective metric spacepartial metric spaceslcsh:QA299.6-433multi-valued mappingslcsh:AnalysisFixed pointFixed-point propertyIntrinsic metricConvex metric spacen-connectedMetric spaceSettore MAT/05 - Analisi Matematicamulti-valued mappingMetric (mathematics)AnalysisMathematics
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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 point results for nonexpansive mappings on metric spaces

2015

In this paper we obtain some fixed point results for a class of nonexpansive single-valued mappings and a class of nonexpansive multi-valued mappings in the setting of a metric space. The contraction mappings in Banach sense belong to the class of nonexpansive single-valued mappings considered herein. These results are generalizations of the analogous ones in Khojasteh et al. [Abstr. Appl. Anal. 2014 (2014), Article ID 325840].

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsGeneral MathematicsFixed pointFixed pointMetric space Multi-valued mapping Picard sequenceMetric spaceSettore MAT/05 - Analisi MatematicaMetric mapSettore MAT/03 - GeometriaCoincidence pointContraction (operator theory)Mathematics
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A homotopy fixed point theorem in 0-complete partial metric space

2015

We generalize a result of Feng and Liu, on multi-valued contractive mappings, for studying the relationship between fixed point sets and homotopy fixed point sets. The presented results are discussed in the generalized setting of 0-complete partial metric spaces. An example and a nonlinear alternative of Leray-Schauder type are given to support our theorems.

Discrete mathematicsHomotopic mappings multi-valued mappings partial metric spacesGeneral MathematicsHomotopyFixed-point theoremProduct metricFixed pointType (model theory)Nonlinear systemMetric spaceSettore MAT/05 - Analisi MatematicaSettore MAT/03 - GeometriaCoincidence pointMathematics
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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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