Results 161 to 170 of about 1,106 (205)
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1997
As we have seen in Chapter I, compactness plays an essential role in the proof of the Schauder fixed point theorem. However, there are some important problems where the operators are not compact.
J. M. Ayerbe Toledano +2 more
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As we have seen in Chapter I, compactness plays an essential role in the proof of the Schauder fixed point theorem. However, there are some important problems where the operators are not compact.
J. M. Ayerbe Toledano +2 more
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1992
In this chapter we consider the basic notions connected with measures of noncompactness (MNCs for brevity) and condensing (or densifying) operators. We define and study in detail the three main and most frequently used MNCs: the Hausdorff MNC χ the Kuratowski MNC α, and the MNC β.
R. R. Akhmerov +4 more
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In this chapter we consider the basic notions connected with measures of noncompactness (MNCs for brevity) and condensing (or densifying) operators. We define and study in detail the three main and most frequently used MNCs: the Hausdorff MNC χ the Kuratowski MNC α, and the MNC β.
R. R. Akhmerov +4 more
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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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Measure of Noncompactness and Spectral Theory
Mathematische Nachrichten, 1984Using the theory of measure of noncompactness the author has extended the results of J. Leray on the spectral theory to the case of noncompact operators in Fréchet spaces. Applying these results the author has estimated the radius of the essential spectrum of operators and has obtained some results in operator theory.
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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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Compactness in measure and measure of noncompactness
Siberian Mathematical Journal, 1997In the class of Banach function spaces with order continuous norm, the author reduces the notion of compactness in measure for a subset of a function space to some equality between two numerical characteristics of the subset.
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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 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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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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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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