Search results for "Schauder fixed point theorem"

showing 10 items of 12 documents

An Integral Version of Ćirić’s Fixed Point Theorem

2011

We establish a new fixed point theorem for mappings satisfying a general contractive condition of integral type. The presented theorem generalizes the well known Ciric's fixed point theorem [Lj. B. Ciric, Generalized contractions and fixed point theorems, Publ. Inst. Math. 12 (26) (1971) 19-26]. Some examples and applications are given.

AlgebraPure mathematicsSchauder fixed point theoremPicard–Lindelöf theoremSettore MAT/05 - Analisi MatematicaGeneral MathematicsFixed-point theoremType (model theory)Fixed pointBrouwer fixed-point theoremKakutani fixed-point theoremComplete metric space $\lambda$-generalized contraction fixed point contractive condition of integral type.MathematicsMediterranean Journal of Mathematics
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On Boundary Conditions for Wedge Operators on Radial Sets

2008

We present a theorem about calculation of fixed point index for k-$\psi$-contractive operators with 0 < k <1 defined on a radial set of a wedge of an infinite dimensional Banach space. Then results on the existence of eigenvectors and nonzero fixed points are obtained.

Control and OptimizationRadial setMathematical analysisBanach spaceFixed-point indexMeasure of noncompactness k-$\psi$-contraction wedge relative fixed point index radial set.Fixed pointFixed-point propertyWedge (geometry)Computer Science ApplicationsSchauder fixed point theoremSettore MAT/05 - Analisi MatematicaSignal ProcessingAnalysisEigenvalues and eigenvectorsMathematicsNumerical Functional Analysis and Optimization
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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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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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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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Shrinking and boundedly complete Schauder frames in Fréchet spaces

2014

We study Schauder frames in Fréchet spaces and their duals, as well as perturbation results. We define shrinking and boundedly complete Schauder frames on a locally convex space, study the duality of these two concepts and their relation with the reflexivity of the space. We characterize when an unconditional Schauder frame is shrinking or boundedly complete in terms of properties of the space. Several examples of concrete Schauder frames in function spaces are also presented.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsShrinkingReflexivitySchauder basisFunction space(LB)-spacesApplied MathematicsMathematics::Analysis of PDEsConvex setMathematics::General TopologyFréchet spacesSchauder basisAtomic decompositionSchauder fixed point theoremSchauder frameLocally convex spacesLocally convex topological vector spaceBoundedly completeDual polyhedronAtomic decompositionMATEMATICA APLICADAAnalysisMathematics
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Fixed point for cyclic weak (\psi, C)-contractions in 0-complete partial metric spaces

2013

In this paper, following (W.A. Kirk, P.S. Srinivasan, P. Veeramani, Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory, 4 (2003), 79-89), we give a fixed point result for cyclic weak (ψ,C)-contractions on partial metric space. A Maia type fixed point theorem for cyclic weak (ψ,C)-contractions is also given.

Discrete mathematicsPure mathematicsMetric spaceSchauder fixed point theoremGeneral MathematicsFixed-point theoremFixed points partial metric spaces weak cyclic φ-contractions.Settore MAT/03 - GeometriaFixed pointType (model theory)Fixed-point propertyMathematics
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Schaefer–Krasnoselskii fixed point theorems using a usual measure of weak noncompactness

2012

Abstract We present some extension of a well-known fixed point theorem due to Burton and Kirk [T.A. Burton, C. Kirk, A fixed point theorem of Krasnoselskii–Schaefer type, Math. Nachr. 189 (1998) 423–431] for the sum of two nonlinear operators one of them compact and the other one a strict contraction. The novelty of our results is that the involved operators need not to be weakly continuous. Finally, an example is given to illustrate our results.

Discrete mathematicsQuantitative Biology::Neurons and CognitionPicard–Lindelöf theoremApplied MathematicsFixed-point theoremFixed-point propertyKrasnoselskii fixed point theoremSchauder fixed point theoremNonlinear integral equationsMeasure of weak noncompactnessBrouwer fixed-point theoremKakutani fixed-point theoremContraction (operator theory)Nonlinear operatorsAnalysisMathematicsJournal of Differential Equations
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On the stability of the Bohl — Brouwer — Schauder Theorem

1996

Discrete mathematicsSchauder fixed point theoremDual spaceApplied MathematicsLocally convex topological vector spaceFixed pointKakutani fixed-point theoremReflexive spaceAnalysisComplete metric spaceTopological vector spaceMathematicsNonlinear Analysis: Theory, Methods &amp; Applications
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Common fixed points of mappings satisfying implicit contractive conditions

2012

In this article we obtain, in the setting of metric spaces or ordered metric spaces, coincidence point, and common fixed point theorems for self-mappings in a general class of contractions defined by an implicit relation. Our results unify, extend, generalize many related common fixed point theorems from the literature. Mathematics Subject Classification (2000): 47H10, 54H25.

Discrete mathematicsimplicit relationApplied MathematicsFixed-point theoremcontractioncommon fixed pointFixed pointFixed-point propertyLeast fixed pointMetric spaceSchauder fixed point theoremcoincidence pointMathematics Subject Classificationfixed pointGeometry and TopologySettore MAT/03 - GeometriaCoincidence pointMathematics
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