Results 131 to 140 of about 498 (162)
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The measure of noncompactness of Sobolev embeddings
Integral Equations and Operator Theory, 1994The author gives new formulas for the upper \(q\)-norm of the embedding \(I: W^ k_ p(Q)\to L_ q(Q)\) \((Q\subset \mathbb{R}^ n)\). She also proves necessary and sufficient conditions for a bounded linear operator to be semi-Fredholm.
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Minimal Sets for a Measure of Noncompactness
1997The notion of a o-minimal set for an MNC o was introduced in [Do1] in order to study the relationships between condensing mappings for Kuratowski and Haus-dorff’s measures of noncompactness (see Chapter X).
J. M. Ayerbe Toledano +2 more
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Strongly Generated Banach Spaces and Measures of Noncompactness
Mathematische Nachrichten, 1998AbstractTo generalize the Hausdorff measure of noncompactness to other classes of bounded sets (like e. g. conditionally weakly compact or Asplund sets), we introduce Grothendieck classes. We deduce integral inequalities for quantities (called Grothendieck measures) related to these classes.
Kunze, Markus, Schlüchtermann, Georg
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Measures of noncompactness in Köthe spaces
Topological Methods in Nonlinear AnalysisIn this paper we introduce some measures of noncompactness and establish estimates between them. Such estimates are helpful to apply fixed point theorems of Darbo-Sadovskiĭ type to compositions of operators. Explicit formulas for calculating these measures of noncompactness are also given, with a particular emphasis on Lebesgue and Orlicz spaces.
Jürgen Appell +4 more
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Compactness Criteria and Measures of Noncompactness in Function Spaces
Journal of the London Mathematical Society, 2000According to a result due to R.S. Phillips, if \((T_s)\) is a net of compact operators converging strongly to the identity, then a bounded set \(A\) in a Banach space is relatively compact if and only if \((T_s)\) converges uniformly on \(A\) to the identity. The aim of this paper is twofold.
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On nullity and fullness of measures of noncompactness
SCIENTIA SINICA Mathematica, 2023Chen Xiaoling, Cheng Lixin, He Wuyi
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On countable determination of the Kuratowski measure of noncompactness
Journal of Mathematical Analysis and Applications, 2021Lixin Cheng, Xiaoling Chen
exaly
The Cauchy-Kovalevsky theorem and noncompactness measures
1997An abstract version of the Cauchy-Kovalevsky theorem for the Cauchy problem \(u'= A(t,u)\), \(u(0) =u_0\) is proved.
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