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Measures of Noncompactness [PDF]

, 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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Measures of noncompactness in Köthe spaces

Topological Methods in Nonlinear Analysis
In 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, Agnieszka Chlebowicz, Tomás Domínguez Benavides, Simon Reinwand, Beata Rzepka   +4 more
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Measures of noncompactness and related properties

2018
AbstractAttempts 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
exaly   +2 more sources

Strongly Generated Banach Spaces and Measures of Noncompactness

Mathematische Nachrichten, 1998
AbstractTo 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.
Markus Kunze
exaly   +3 more sources

On some measures of noncompactness in the space of continuous functions

Nonlinear Analysis: Theory, Methods & Applications, 2008
We consider some quantities in the space of functions continuous on a bounded interval, which are related to monotonicity of functions. Based on those quantities we construct a few measures of noncompactness in the mentioned function space.
Józef Banas, Kishin Sadarangani
exaly   +2 more sources

Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations

, 2014
This book deals with the study of sequence spaces, matrix transformations, measures of noncompactness and their various applications. The notion of measure of noncompactness is one of the most useful ones available and has many applications.
Józef Banas, M Mursaleen
exaly   +2 more sources

Measures of Noncompactness

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, T. Domínguez Benavides, G. López Acedo   +2 more
openaire   +1 more source

Theorems of ascoli type involving measures of noncompactness

Nonlinear Analysis: Theory, Methods & Applications, 1981
Hans-Peter Heinz
exaly   +3 more sources

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.
openaire   +1 more source

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.
openaire   +1 more source