Search results for "convex"

showing 10 items of 389 documents

A note on best approximation in 0-complete partial metric spaces

2014

We study the existence and uniqueness of best proximity points in the setting of 0-complete partial metric spaces. We get our results by showing that the generalizations, which we have to consider, are obtained from the corresponding results in metric spaces. We introduce some new concepts and consider significant theorems to support this fact.

Discrete mathematicsArticle SubjectApplied MathematicsInjective metric spacelcsh:MathematicsT-normlcsh:QA1-939Intrinsic metricConvex metric spaceUniform continuityMetric spaceFréchet spaceSettore MAT/05 - Analisi Matematica0-completeness best proximity point fixed point partial metric spaceMetric (mathematics)AnalysisMathematics
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Common Fixed Points in a Partially Ordered Partial Metric Space

2013

In the first part of this paper, we prove some generalized versions of the result of Matthews in (Matthews, 1994) using different types of conditions in partially ordered partial metric spaces for dominated self-mappings or in partial metric spaces for self-mappings. In the second part, using our results, we deduce a characterization of partial metric 0-completeness in terms of fixed point theory. This result extends the Subrahmanyam characterization of metric completeness.

Discrete mathematicsArticle SubjectInjective metric spacelcsh:MathematicsEquivalence of metricslcsh:QA1-939Fixed points dominated self-mappings 0-completenessConvex metric spaceIntrinsic metricCombinatoricsMetric spaceSettore MAT/05 - Analisi MatematicaMetric (mathematics)Metric differentialFisher information metricMathematicsInternational Journal of Analysis
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On a theorem of Khan in a generalized metric space

2013

Existence and uniqueness of fixed points are established for a mapping satisfying a contractive condition involving a rational expression on a generalized metric space. Several particular cases and applications as well as some illustrative examples are given.

Discrete mathematicsArticle Subjectlcsh:MathematicsInjective metric spacerational expression.Pseudometric spaceFixed pointFixed pointlcsh:QA1-939Convex metric spaceMetric spaceSettore MAT/05 - Analisi MatematicaMetric (mathematics)Uniquenessgeneralized metric spaceMetric differentialMathematics
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Fixed Points for Weakα-ψ-Contractions in Partial Metric Spaces

2013

Recently, Samet et al. (2012) introduced the notion ofα-ψ-contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notion of weakα-ψ-contractive mappings and give fixed point results for this class of mappings in the setting of partial metric spaces. Also, we deduce fixed point results in ordered partial metric spaces. Our results extend and generalize the results of Samet et al.

Discrete mathematicsClass (set theory)Metric spacePure mathematicsApplied MathematicsInjective metric spaceMetric mapProduct metricFixed pointAnalysisMathematicsIntrinsic metricConvex metric spaceAbstract and Applied Analysis
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Analytic Extension of Non Quasi - Analytic Whitney Jets of Beurling Type

1998

Let (Mr)r∈ℕ0 be a logarithmically convex sequence of positive numbers which verifies M0 = 1 as well as Mr ≥ 1 for every r ∈ ℕ and defines a non quasi - analytic class. Let moreover F be a closed proper subset of ℝn. Then for every function f on ℝn belonging to the non quasi - analytic (Mr)-class of Beurling type, there is an element g of the same class which is analytic on ℝ,nF and such that Dαf(x) = Dαg(x) for every α ∈ ℕn0 and x ∈ F.

Discrete mathematicsClass (set theory)Pure mathematicsSequenceLogarithmically convex functionGeneral MathematicsExtension (predicate logic)Function (mathematics)Element (category theory)Type (model theory)MathematicsMathematische Nachrichten
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Vector-valued meromorphic functions

2002

A locally complete locally convex space E satisfies that every weakly meromorphic function defined on an open subset of \( \mathbb{C} \) with values in E is meromorphic if and only if E does not contain a countable product of copies of \( \mathbb{C} \). A characterization of locally complete spaces in the spirit of known characterizations of the (metric) convex compactness property is also given.

Discrete mathematicsCompact spaceGeneral MathematicsProduct (mathematics)Regular polygonConvex setCountable setCharacterization (mathematics)Complete metric spaceMeromorphic functionMathematics
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On generalized weakly G-contraction mapping in G-metric spaces

2011

In this paper, we establish some common fixed point results for two self-mappings f and g on a generalized metric space X. To prove our results we assume that f is a generalized weakly G-contraction mapping of types A and B with respect to g.

Discrete mathematicsComputational MathematicsMetric spaceComputational Theory and MathematicsModeling and SimulationInjective metric spaceMetric (mathematics)Metric mapProduct metricContraction mappingIntrinsic metricMathematicsConvex metric spaceComputers & Mathematics with Applications
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Common fixed points in generalized metric spaces

2012

Abstract We establish some common fixed point theorems for mappings satisfying a ( ψ , φ ) -weakly contractive condition in generalized metric spaces. Presented theorems extend and generalize many existing results in the literature.

Discrete mathematicsComputational MathematicsMetric spaceFixed-point iterationSettore MAT/05 - Analisi MatematicaApplied MathematicsGeneralized metric weakly contractive condition contraction of integral type fixed point common fixed points.Common fixed pointProduct metricFixed pointIntrinsic metricMathematicsConvex metric space
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Some Questions of Heinrich on Ultrapowers of Locally Convex Spaces

1993

In this note we treat some open problems of Heinrich on ultrapowers of locally convex spaces. In section 1 we investigate the localization of bounded sets in the full ultrapower of a locally convex space, in particular the coincidence of the full and the bounded ultrapower, mainly concentrating in the case of (DF)-spaces. In section 2 we provide a partial answer to a question of Heinrich on commutativity of strict inductive limits and ultrapowers. In section 3 we analyze the relation between some natural candidates for the notion of superreflexivity in the setting of Frechet spaces. We give an example of a Frechet-Schwartz space which is not the projective limit of a sequence of superreflex…

Discrete mathematicsConvex analysisMathematics::Functional AnalysisPure mathematicsSequenceGeneral MathematicsBanach spaceConvex setUltraproductSpace (mathematics)Mathematics::LogicBounded functionLocally convex topological vector spaceMathematicsMathematische Nachrichten
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Approximate convex hull of affine iterated function system attractors

2012

International audience; In this paper, we present an algorithm to construct an approximate convex hull of the attractors of an affine iterated function system (IFS). We construct a sequence of convex hull approximations for any required precision using the self-similarity property of the attractor in order to optimize calculations. Due to the affine properties of IFS transformations, the number of points considered in the construction is reduced. The time complexity of our algorithm is a linear function of the number of iterations and the number of points in the output convex hull. The number of iterations and the execution time increases logarithmically with increasing accuracy. In additio…

Discrete mathematicsConvex hull0209 industrial biotechnologyGeneral MathematicsApplied Mathematics010102 general mathematicsProper convex functionConvex setMathematicsofComputing_GENERALGeneral Physics and AstronomyStatistical and Nonlinear Physics02 engineering and technology[ INFO.INFO-GR ] Computer Science [cs]/Graphics [cs.GR]01 natural sciences[INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR]020901 industrial engineering & automationAffine hullTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYConvex polytopeOutput-sensitive algorithmConvex combination0101 mathematicsConvex conjugateMathematics
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