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Measures of noncompactness of interpolated polynomials
Forum Mathematicum, 2022Abstract We study interpolation of the measure of noncompactness of homogeneous polynomials on Banach spaces. We prove that, for a large class of interpolation functors, preserving interpolation of measures of noncompactness of interpolated linear operators between Banach couples can be lifted to polynomials.
Mastyło, Mieczysław +1 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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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 controllability and measures of noncompactness
AIP Conference Proceedings, 2014This article deals with an infinitely dimensional nonlinear dynamical systems given in a state space form. Among such systems we distinguish a wide class of semilinear systems, for which we present a set of controllability conditions. These conditions for controllability are based on a fixed point theorems and measures of noncompactness.
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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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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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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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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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