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SECOND ORDER SEMILINEAR EVOLUTION EQUATIONS WITH INFINITE DELAY VIA MEASURE OF NONCOMPACTNESS
M Benchohra +38 more
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Fixed point free maps of a closed ball with small measures of noncompactness
Martin Väth
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Weighted Estimates of a Measure of Noncompactness for Maximal and Potential Operators
Meskhi Alexander, Muhammad Asif
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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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Inequivalent measures of noncompactness
Annali di Matematica Pura ed Applicata, 2010Let \(X\) be a Banach space and \({\mathcal B}(X)\) denote the set of all bounded subsets of \(X\). We say that a map \(\beta:{\mathcal B}(X)\to [0,\infty)\) is a homogeneous measure of noncompactness on \(X\) if for all \(S,T\in{\mathcal B}(X)\): (1) \(\beta(S)= 0\) iff \(\overline S\) is compact, (2) \(\beta(S)\leq\beta(T)\) for all \(S\subset T ...
Mallet-Paret, John, Nussbaum, Roger D.
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On measures of weak noncompactness
Annali di Matematica Pura ed Applicata, 1988The authors give an axiomatic definition of measures of weak noncompactness which is in some sense parallel to \textit{B. N. Sadovskij}'s definition of measures of (strong) noncompactness [see e.g. Usp. Mat. Nauk 27, No.1, 81-146 (1972; Zbl 0243.47033)]. The first explicit measure of weak noncompactness is due to \textit{F. S. de Blasi} [Bull.
Banaś, Józef, Rivero, Jesus
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