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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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On measures of weak noncompactness
Publicationes Mathematicae Debrecen, 1994A notion of measure of weak noncompactness is introduced which generalizes the De Blasi measure of weak noncompactness. Some properties of this generalized measure are proved. The existence of bounded weak solutions of certain differential equations is shown.
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Matrix Transformations and Measures of Noncompactness
2021The major part of this chapter is introductory and included as a reference for the reader’s convenience; it recalls the concepts and results from the theories of sequence spaces, matrix transformations in Sects. 1.1–1.3, and 1.5 and measures of noncompactness in Sects. 1.7–1.10 that are absolutely essential for the book.
Bruno de Malafosse +2 more
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The measure of noncompactness of multilinear operators
Nonlinear Analysis, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Vakhtang Kokilashvili +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 and related properties
2018AbstractAttempts to classify properties of the ball B, or the space X, utilizing the notion of measures of noncompactness are presented. They are connected with the Kadec–Klee property. Measures of noncompactness are used to generalize the notion of uniform convexity and smoothness.
Kazimierz Goebel, Stanisław Prus
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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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Kuratowski's Measure of Noncompactness with Respect to Thompson's Metric
Zeitschrift für Analysis und ihre Anwendungen, 2014It is known that the interior of a normal cone K in a Banach space is a complete metric space with respect to Thompson's metric d .
Herzog, Gerd, Kunstmann, Peer Christian
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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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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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