Book Review: Measures of noncompactness and condensing operators
نویسندگان
چکیده
منابع مشابه
Inequivalent measures of noncompactness
Two homogeneous measures of noncompactness β and γ on an infinite dimensional Banach space X are called “equivalent” if there exist positive constants b and c such that bβ(S) ≤ γ (S) ≤ cβ(S) for all bounded sets S ⊂ X . If such constants do not exist, the measures of noncompactness are “inequivalent.”Weask a foundational questionwhich apparently has not previously been considered: For what infi...
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in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...
15 صفحه اولSolving infinite system of nonlinear integral equations by using F-generalized Meir-Keeler condensing operators, measure of noncompactness and modified homotopy perturbation.
In this article to prove existence of solution of infinite system of nonlinear integral equations, we consider the space of solution containing all convergence sequences with a finite limit, as with a suitable norm is a Banach space. By creating a generalization of Meir-Keeler condensing operators which is named as F-generalized Meir-Keeler condensing operators and measure of noncompactness, we...
متن کاملConstruction of measures of noncompactness of $C^k(Omega)$ and $C^k_0$ and their application to functional integral-differential equations
In this paper, first, we investigate the construction of compact sets of $ C^k$ and $ C_0^k$ by proving ``$C^k, C_0^k-version$" of Arzel`{a}-Ascoli theorem, and then introduce new measures of noncompactness on these spaces. Finally, as an application, we study the existence of entire solutions for a class of the functional integral-differential equations by using Darbo's fixe...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1994
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1994-00461-6