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Measures of Noncompactness and Their Applications
2017In this chapter, we present a survey of theory and applications of measures of noncompactness. The standard measures of noncompactness are discussed and their properties are compared. Some results concerning standard measures of noncompactness in different spaces including \(C([a,b];\mathbb {R})\), \(L^p([a,b];\mathbb {R})\), Banach spaces with ...
Mohammad Mursaleen +2 more
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Compactness by the Hausdorff measure of noncompactness
Nonlinear Analysis: Theory, Methods & Applications, 2010A linear subspace \(X\) of the space of all complex sequences, denoted by \(w\), is called a \(BK\)-space if it is a Banach space with continuous coordinates \(p_{n}: X \to \mathbb{C}\) \((n\in \mathbb{N})\), where \(\mathbb{C}\) is the complex field and \(p_{n}(x)=x_{n}\) for all \(x=(x_{k})\in X\).
Mursaleen, M., Noman, Abdullah K.
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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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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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Impulsive integrodifferential Equations and Measure of noncompactness
2016This paper is concerned with the existence of mild solutions for impulsive integro-differential equations with nonlocal conditions. We apply the technique measure of noncompactness in the space of piecewise continuous functions and by using Darbo-Sadovskii's fixed point theorem, we prove reasults about impulsive integro-differential equations for ...
Valipour Baboli, Alireza, Ghaemi, M.B.
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On Some Results Using Measures of Noncompactness
2017In this chapter, we review some results on measures of noncompactness, including an axiomatic introduction, a study of the Kuratowski, Hausdorff, inner Hausdorff and separation measures of noncompactness, a survey of their most important properties and their roles in fixed-point theory and operator theory.
Eberhard Malkowsky, Vladimir Rakočević
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Time to add screening for financial hardship as a quality measure?
Ca-A Cancer Journal for Clinicians, 2021Cathy J Bradley +2 more
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A minimal common outcome measure set for COVID-19 clinical research
Lancet Infectious Diseases, The, 2020Srinivas Murthy +2 more
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