Results 121 to 130 of about 490 (162)

Measures of Noncompactness

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, M. I. Kamenskii, A. S. Potapov, A. E. Rodkina, B. N. Sadovskii   +4 more
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Measure of Noncompactness and Spectral Theory

Mathematische Nachrichten, 1984
Using 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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Compactness in measure and measure of noncompactness

Siberian Mathematical Journal, 1997
In 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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Measures of noncompactness of interpolated polynomials

Forum Mathematicum, 2022
Abstract 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, da Silva, Eduardo Brandani   +1 more
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On measures of weak noncompactness

Publicationes Mathematicae Debrecen, 1994
A 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

2017
In 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, Syed M. H. Rizvi, Bessem Samet   +2 more
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On controllability and measures of noncompactness

AIP Conference Proceedings, 2014
This 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

2021
The 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, Eberhard Malkowsky, Vladimir Rakočević   +2 more
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The measure of noncompactness of multilinear operators

Nonlinear Analysis, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Vakhtang Kokilashvili, Mieczysław Mastyło, Alexander Meskhi   +2 more
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Compactness by the Hausdorff measure of noncompactness

Nonlinear Analysis: Theory, Methods & Applications, 2010
A 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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