Search results for "Theorem"

showing 10 items of 1250 documents

Fixed point theory in partial metric spaces via φ-fixed point’s concept in metric spaces

2014

Abstract Let X be a non-empty set. We say that an element x ∈ X is a φ-fixed point of T, where φ : X → [ 0 , ∞ ) and T : X → X , if x is a fixed point of T and φ ( x ) = 0 . In this paper, we establish some existence results of φ-fixed points for various classes of operators in the case, where X is endowed with a metric d. The obtained results are used to deduce some fixed point theorems in the case where X is endowed with a partial metric p. MSC:54H25, 47H10.

Discrete mathematicsInjective metric spaceApplied Mathematicsmetric spacepartial metric spaceFixed-point theoremFixed pointFixed-point propertyIntrinsic metricConvex metric spaceIsolated pointMetric spacefixed pointSettore MAT/05 - Analisi MatematicaDiscrete Mathematics and Combinatorics$\varphi$-fixed pointAnalysisMathematicsJournal of Inequalities and Applications
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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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A decomposition theorem for compact-valued Henstock integral

2006

We prove that if X is a separable Banach space, then a measurable multifunction Γ : [0, 1] → ck(X) is Henstock integrable if and only if Γ can be represented as Γ = G + f, where G : [0, 1] → ck(X) is McShane integrable and f is a Henstock integrable selection of Γ.

Discrete mathematicsIntegrable systemSelection (relational algebra)MultifunctionHenstock integralIf and only ifGeneral MathematicsBanach spacePettis integralKurzweil–Henstock–Pettis integral selectionSeparable spaceMathematicsDecomposition theorem
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On Rough Sets in Topological Boolean Algebras

1994

We have focused on rough sets in topological Boolean algebras. Our main ideas on rough sets are taken from concepts of Pawlak [4] and certain generalizations of his constructions which were offered by Wiweger [7]. One of the most important results of this note is a characterization of the rough sets determined by regular open and regular closed elements.

Discrete mathematicsInterior algebraRough setField of setsBoolean algebras canonically definedCharacterization (mathematics)Stone's representation theorem for Boolean algebrasTopologyComplete Boolean algebraMathematics
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Law of the Iterated Logarithm

2020

For sums of independent random variables we already know two limit theorems: the law of large numbers and the central limit theorem. The law of large numbers describes for large \(n\in \mathbb{N}\) the typical behavior, or average value behavior, of sums of n random variables. On the other hand, the central limit theorem quantifies the typical fluctuations about this average value.

Discrete mathematicsIterated logarithmNatural logarithm of 2LogarithmLaw of large numbersLaw of the iterated logarithmLimit (mathematics)Random variableMathematicsCentral limit theorem
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Unified Metrical Common Fixed Point Theorems in 2-Metric Spaces via an Implicit Relation

2013

We prove some common fixed point theorems for two pairs of weakly compatible mappings in 2-metric spaces via an implicit relation. As an application to our main result, we derive Bryant's type generalized fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results. Moreover, we study the existence of solutions of a nonlinear integral equation.

Discrete mathematicsLeast fixed point2-metric space common property (E.A) common limit range property weakly compatible mappings implicit relations fixed point.Metric spaceSchauder fixed point theoremArticle SubjectSettore MAT/05 - Analisi MatematicaFixed-point theoremType (model theory)Fixed-point propertyCoincidence pointFinite setMathematicsJournal of Operators
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A fixed point theorem inG-metric spaces viaα-series

2014

In the context of G -metric spaces we prove a common fixed point theorem for a sequence of self mappings using a new concept of α-series. Keywords: α-series, common fixed point, G -metric space Quaestiones Mathematicae 37(2014), 429-434

Discrete mathematicsLeast fixed pointMetric spaceMathematics (miscellaneous)Fréchet spaceFixed-point theoremFixed-point propertyBrouwer fixed-point theoremKakutani fixed-point theoremCoincidence pointMathematicsQuaestiones Mathematicae
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A property of connected Baire spaces

1997

Abstract We give a topological version of a classical result of F. Sunyer Balaguer's on a local characterization of real polynomials. This is done by studying a certain property on a class of connected Baire spaces, thus allowing us to obtain a local characterization of repeated integrals of analytic maps on Banach spaces.

Discrete mathematicsLocally connectedBanach spaceBaire category theoremGeometry and TopologyBaire spaceBaire spaceOpen mapping theorem (functional analysis)Baire measureSunyer Balaguer's TheoremComplete metric spaceMathematicsTopology and its Applications
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Subgroups of $$SF(\omega )$$ S F ( ω ) and the relation of almost containedness

2016

The relations of almost containedness and orthogonality in the lattice of groups of finitary permutations are studied in the paper. We define six cardinal numbers naturally corresponding to these relations by the standard scheme of $$P(\omega )$$P(ź). We obtain some consistency results concerning these numbers and some versions of the Ramsey theorem.

Discrete mathematicsLogic010102 general mathematics0102 computer and information sciencesLattice (discrete subgroup)01 natural sciencesOmegaCombinatoricsMathematics::LogicPhilosophyOrthogonality010201 computation theory & mathematicsConsistency (statistics)Scheme (mathematics)FinitaryRamsey's theorem0101 mathematicsRelation (history of concept)MathematicsArchive for Mathematical Logic
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