Search results for "cone metric space."

showing 10 items of 23 documents

A coincidence-point problem of Perov type on rectangular cone metric spaces

2017

We consider a coincidence-point problem in the setting of rectangular cone metric spaces. Using alpha-admissible mappings and following Perov's approach, we establish some existence and uniqueness results for two self-mappings. Under a compatibility assumption, we also solve a common fixed-point problem.

Algebra and Number Theory010102 general mathematicsMathematical analysisGeometryType (model theory)01 natural sciencesRectangular cone metric space spectral radius solid cone g-contraction of Perov type -admissible mapping -g-contraction of Perov type010101 applied mathematicsMetric spaceCone (topology)Settore MAT/05 - Analisi MatematicaSettore MAT/03 - Geometria0101 mathematicsCoincidence pointAnalysisMathematicsThe Journal of Nonlinear Sciences and Applications
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Nonlinear quasi-contractions of Ciric type

2012

In this paper we obtain points of coincidence and common fixed points for two self mappings satisfying a nonlinear contractive condition of Ciric type. As application, using the scalarization method of Du, we deduce a result of common fixed point in cone metric spaces.

Common fixed points quasi-contractions scalarization cone metric spaces.Settore MAT/05 - Analisi Matematica
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$varphi$-pairs and common fixed points in cone metric spaces

2008

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

Cone metric spaces \and $\varphi$-pairs \and Common fixed points \and Coincidence pointsPure mathematicsGeneral MathematicsInjective metric spaceMathematical analysisFixed pointIntrinsic metricConvex metric spaceMetric spaceCone (topology)Settore MAT/05 - Analisi MatematicaMetric (mathematics)Metric mapMathematics
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Common fixed points in cone metric spaces for CJM-pairs

2011

Abstract In this paper we introduce some contractive conditions of Meir–Keeler type for two mappings, called f - M K -pair mappings and f - C J M -pair (from Ciric, Jachymski, and Matkowski) mappings, in the framework of regular cone metric spaces and we prove theorems which guarantee the existence and uniqueness of common fixed points. We give also a fixed point result for a multivalued mapping that satisfies a contractive condition of Meir–Keeler type. These results extend and generalize some recent results from the literature. To conclude the paper, we extend our main result to non-regular cone metric spaces by using the scalarization method of Du.

Cone metric spaces CJM-pairs Common fixed points Common coincidence points.Injective metric spaceMathematical analysisMathematics::General TopologyFixed pointComputer Science ApplicationsIntrinsic metricConvex metric spaceCombinatoricsMetric spaceCone (topology)Settore MAT/05 - Analisi MatematicaModeling and SimulationUniquenessCoincidence pointMathematicsMathematical and Computer Modelling
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Invariant approximation results in cone metric spaces

2011

‎Some sufficient conditions for the existence of fixed point of mappings‎ ‎satisfying generalized weak contractive conditions is obtained‎. ‎A fixed‎ ‎point theorem for nonexpansive mappings is also obtained‎. ‎As an application‎, ‎some invariant approximation results are derived in cone metric spaces‎.

Control and OptimizationAlgebra and Number TheoryInjective metric spaceTangent coneMathematical analysis‎non normal cone‎54C60‎54H25‎‎orbitally continuous‎cone metric spacesIntrinsic metricConvex metric spaceFixed pointsMetric space‎46B40Dual cone and polar coneSettore MAT/05 - Analisi MatematicaMetric map‎invariant‎ ‎approximationInvariant (mathematics)Fixed points orbitally continuous invariant approximation cone metric spaces non normal cone.47H10AnalysisMathematics
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Coupled fixed point, F-invariant set and fixed point of N-order

2010

‎In this paper‎, ‎we establish some new coupled fixed point theorems in complete metric spaces‎, ‎using a new concept of $F$-invariant set‎. ‎We introduce the notion of fixed point of $N$-order as natural extension of that of coupled fixed point‎. ‎As applications‎, ‎we discuss and adapt the presented results to the setting of partially ordered cone metric spaces‎. ‎The presented results extend and complement some known existence results from the literature‎.

Discrete mathematicsCoupled fixed point F-invariant set fixed point of N-order partially ordered set cone metric spaceControl and OptimizationAlgebra and Number Theory47H10‎Fixed-point theoremFixed pointFixed-point propertyCoupled fixed point‎partially ordered setLeast fixed point‎$F$-invariant set54H25Schauder fixed point theoremFixed-point iterationSettore MAT/05 - Analisi Matematica‎34B15‎cone metric space‎fixed point of $N$-orderKakutani fixed-point theoremAnalysisHyperbolic equilibrium pointMathematics
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Edelstein-Suzuki-type resuls for self-mappings in various abstract spaces with application to functional equations

2016

Abstract The fixed point theory provides a sound basis for studying many problems in pure and applied sciences. In this paper, we use the notions of sequential compactness and completeness to prove Eldeisten-Suzuki-type fixed point results for self-mappings in various abstract spaces. We apply our results to get a bounded solution of a functional equation arising in dynamic programming.

G-metric spaceG-cone metric spaceBasis (linear algebra)General Mathematics010102 general mathematicsquasi-metric spaceGeneral Physics and AstronomyFixed-point theoremFixed pointType (model theory)Edelstein’s theorem01 natural sciences010101 applied mathematicsAlgebraCompact spacefixed pointSettore MAT/05 - Analisi MatematicaBounded functionCompleteness (order theory)Functional equation0101 mathematicsSuzuki’s theorem.Mathematics
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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 \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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Fixed point results for $G^m$-Meir-Keeler contractive and $G$-$(\alpha,\psi)$-Meir-Keeler contractive mappings

2013

In this paper, first we introduce the notion of a $G^m$-Meir-Keeler contractive mapping and establish some fixed point theorems for the $G^m$-Meir-Keeler contractive mapping in the setting of $G$-metric spaces. Further, we introduce the notion of a $G_c^m$-Meir-Keeler contractive mapping in the setting of $G$-cone metric spaces and obtain a fixed point result. Later, we introduce the notion of a $G$-$(\alpha,\psi)$-Meir-Keeler contractive mapping and prove some fixed point theorems for this class of mappings in the setting of $G$-metric spaces.

Settore MAT/05 - Analisi Matematica$G^m$-Meir-Keeler contractive mapping $G$-metric space $G_c^m$-Meir-Keeler contractive mapping $G$-Cone metric space $G$-$(\alpha\psi)$-Meir-Keeler contractive mapping
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