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The Concept of Measures of Noncompactness in Banach Spaces

Symmetry
This article is a survey, and its aim is to provide a concise introduction to the topic of measures of noncompactness and measures of weak noncompactness in Banach spaces. These measures constitute a useful tool in nonlinear analysis, for example, in studies on the existence of solutions to nonlinear differential and integral equations.
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The measure of noncompactness of multilinear operators

Nonlinear Analysis, 2019
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Vakhtang Kokilashvili, Mieczysław Mastyło, Alexander Meskhi   +2 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
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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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Minimal Sets for a Measure of Noncompactness

1997
The 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, T. Domínguez Benavides, G. López Acedo   +2 more
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Kuratowski's Measure of Noncompactness with Respect to Thompson's Metric

Zeitschrift für Analysis und ihre Anwendungen, 2014
It 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, 1994
The 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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Tripled Fixed Points and Existence Study to a Tripled Impulsive Fractional Differential System via Measures of Noncompactness

Mathematics, 2022
Maria Alessandra Ragusa, Sina Etemad, Mohammed M Matar   +2 more
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On nullity and fullness of measures of noncompactness

SCIENTIA SINICA Mathematica, 2023
Chen Xiaoling, Cheng Lixin, He Wuyi
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Results on the Existence of Hilfer Fractional Neutral Evolution Equations With Infinite Delay via Measures of Noncompactness

Mathematical Methods in the Applied Sciences, 2021
Kottakkaran Sooppy Nisar, Velusamy Vijayakumar, R Udhayakumar   +2 more
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