Search results for "Measure of weak noncompactness"

showing 3 items of 3 documents

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 some parameters related to weak noncompactness in L1(μ,E)

2009

A weak measure of noncompactness γU is defined in a Banach space in terms of convex compactness. We obtain relationships between the measure γU(A) of a bounded set A in the Bochner space L1(μ,E) and two parameters Π(A) and Λ1(A).

Settore MAT/05 - Analisi MatematicaBochner integrable function weak compactness w-tightness measure of weak noncompactness.
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On some parameters related to weak noncompactness in L1(μ,E)

2009

A measure of weak noncompactness γU is defined in a Banach space X in terms of convex compactness. We obtain relationships between the measure γU(A) of a bounded set A in the Bochner space L1(μ,E) and two parameters Π(A) and Λ1(A) related, respectively, to uniform integrability and weak-tightness. The criterion for relative weak compactness in L1(μ,E) is recovered.

Settore MAT/05 - Analisi MatematicaWeak compactness w-tightness measure of weak noncompactness.
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