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- W4310267009 abstract "This paper is devoted to studying the representation of measures of non-generalized compactness, in particular, measures of noncompactness, of non-weak compactness and of non-super weak compactness, etc., defined on Banach spaces and its applications. With the aid of a three-time order-preserving embedding theorem, we show that for every Banach space X, there exist a Banach function space C(K) for some compact Hausdorff space K and an order-preserving affine mapping $$mathbb{T}$$ from the super space $${cal B}$$ of all the nonempty bounded subsets of X endowed with the Hausdorff metric to the positive cone C(K)+ of C(K) such that for every convex measure, in particular, the regular measure, homogeneous measure and sublinear measure of non-generalized compactness μ on X, there is a convex function F on the cone $$V = mathbb{T}left( {cal B} right)$$ which is Lipschitzian on each bounded set of V such that $$digammaleft(mathbb{T}{left( B right)} right) = mu left( B right),,,,,,,forall ,B in {cal B}$$ As its applications, we show a class of basic integral inequalities related to an initial value problem in Banach spaces, and prove a solvability result of the initial value problem, which is an extension of some classical results due to Banaś and Goebel (1980), Goebel and Rzymowski (1970) and Rzymowski (1971)." @default.
- W4310267009 created "2022-11-30" @default.
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- W4310267009 date "2022-11-24" @default.
- W4310267009 modified "2023-10-18" @default.
- W4310267009 title "Representation of measures of noncompactness and its applications related to an initial value problem in Banach spaces" @default.
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- W4310267009 doi "https://doi.org/10.1007/s11425-022-1986-x" @default.
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