Representation of measures of noncompactness and its applications related to an initial value problem in Banach spaces

نویسندگان

چکیده

This paper is devoted to studying the representation of measures non-generalized compactness, in particular, noncompactness, non-weak compactness and non-super weak etc., defined on Banach spaces its applications. With aid a three-time order-preserving embedding theorem, we show that for every space X, there exist function C(K) some compact Hausdorff K an affine mapping $$\mathbb{T}$$ from super $${\cal B}$$ all nonempty bounded subsets X endowed with metric positive cone C(K)+ such convex measure, regular homogeneous measure sublinear μ F $$V = \mathbb{T}\left( {\cal B} \right)$$ which Lipschitzian each set V $$\digamma\left(\mathbb{T}{\left( B \right)} \right) \mu \left( \right),\,\,\,\,\,\,\forall \,B \in As applications, class basic integral inequalities related initial value problem spaces, prove solvability result problem, extension classical results due Banaś Goebel (1980), Rzymowski (1970) (1971).

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ژورنال

عنوان ژورنال: Science China-mathematics

سال: 2022

ISSN: ['1674-7283', '1869-1862']

DOI: https://doi.org/10.1007/s11425-022-1986-x