Sublinear bilipschitz equivalence and the quasiisometric classification of solvable Lie groups
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract We prove a product theorem for sublinear bilipschitz equivalences which generalizes the classical work of Kapovich, Kleiner, and Leeb on quasiisometries between product spaces. We employ our product theorem to distinguish up to quasiisometry certain families of solvable groups which share the same dimension, cone‐dimension and Dehn function ...
Ido Grayevsky, Gabriel Pallier
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An application of a measure of noncompactness in the study of asymptotic stability [PDF]
, 2003 Using the technique of fixed-point theorem of Darbo type associated with measures of noncompactness, we obtain an existence result for some functional-integral equation. Moreover, the choice of suitable measure of noncompactness allows us to characterize
Banaś, J., Rzepka, B.
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Measures of noncompactness and their applications
, 2021 The measures of noncompactness are very useful tools in the theory of operatorequations in Banach spaces. In particular, the fixed point theorems derived fromthem have many important results. In this study, we state a general information onmeasures of noncompactness and fixed point theory. In addition, applications fromvarious topics are presented.
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Semigroups of operators and measures of noncompactness
Journal of Functional Analysis, 1971 AbstractIt is observed that the perturbation class of an open semigroup in a Banach algebra is a closed two-sided ideal. Certain seminorms on the algebra of bounded operators are introduced; these seminorms induce norms on the quotient algebra modulo the ideal of compact operators.
Lebow, Arnold, Schechter, Martin
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Measures of noncompactness in Hilbert $C^*$-modules [PDF]
Consider a countably generated Hilbert $C^*$-module $\mathcal M$ over a $C^*$-algebra $\mathcal A$. There is a measure of noncompactness $λ$ defined, roughly as the distance from finitely generated projective submodules, which is independent of any ...
Kečkić, Dragoljub J., Lazović, Zlatko
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Applications of the Hausdorff measure of noncompactness in some sequence spaces of weighted means [PDF]
, 2010 In the present paper, we establish some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain operators on some sequence spaces of weighted means.
Mursaleen, M. +3 more
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On matrix transformations and Hausdorff measure of noncompactness of Euler difference sequence spaces of fractional order [PDF]
, 2021 In the present paper, some results on matrix mappings and Hausdorff measure of noncompactness of certain generalized Euler difference sequence spaces of fractional order are discussed.
Kadak, Ugur, Baliarsingh, P.
core
Fractional dynamic system simulating the growth of microbe. [PDF]
Adv Differ Equ, 2021 Hadid SB, Ibrahim RW.
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Convergence Theorems and Measures of Noncompactness for Noncompact Urysohn Operators in Ideal Spaces
Journal of Integral Equations and Applications, 2004 The author considers the following nonlinear integral equation of Urysohn type \[ A(f)x(t):= \int_S f(t, s,x(s))\,ds,\quad t\in T, \] where the integral is in the Bochner sense. He establishes an estimate for the measure of noncompactness of the Urysohn operator and proves a convergence theorem for a sequence of simpler Urysohn operators which are ...
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Existence of solutions for a fractional hybrid boundary value problem via measures of noncompactness in Banach algebras [PDF]
, 2014 We study the existence of solutions for the following fractional hybrid boundary value problem where 1< α≤ 2 and D α 0+ denotes the Riemann-Liouville fractional derivative.
Sadarangani, Kishin +2 more
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