Search results for "Fixed-point index"

showing 3 items of 3 documents

An extension of Guo's theorem via k--contractive retractions

2006

Abstract Let X be a infinite-dimensional Banach space. We generalize Guo's Theorem [D.J. Guo, Eigenvalues and eigenvectors of nonlinear operators, Chinese Ann. Math. 2 (1981) 65–80 [English]] to k- ψ -contractions and condensing mappings, under a condition which depends on the infimum k ψ of all k ⩾ 1 for which there exists a k- ψ -contractive retraction of the closed unit ball of the space X onto its boundary.

Unit spherePure mathematicsApplied MathematicsMathematical analysisFixed-point indexBanach spaceInfimum and supremumAnalysisEigenvalues and eigenvectorsNonlinear operatorsMathematicsNonlinear Analysis: Theory, Methods & Applications
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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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Eigenvectors of k–ψ-contractive wedge operators

2008

Abstract We present new boundary conditions under which the fixed point index of a strict- ψ -contractive wedge operator is zero. Then we investigate eigenvalues and corresponding eigenvectors of k – ψ -contractive wedge operators.

Operator (computer programming)Applied MathematicsRadial setMathematical analysisFixed-point indexBoundary value problemOperator theoryWedge (geometry)Eigenvalues and eigenvectorsMathematicsApplied Mathematics Letters
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