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it is easy to check that pc([0, t]; x) is a banach space with the norm ||u||pc = sup{||u (t)||, t Î [0, t]} and c([0, t]; x) ⊆ pc([0, t]; x) ⊆ l1 ([0, t]; x). moreover, we denote b by the hausdorff measure of noncompactness of x, denote bc by the hausdorff measure of noncompactness of c ([0, t]; x) and denote bpc by the hausdorff measure of noncompactness of pc([0, t]; x).
pc-nin ([0, t]; x) norması || u || pc = sup {|| u (t) ||, t Î [0, t]} və bir banach boşluğu olduğunu yoxlamaq asandır. c ([0, t]; x) ⊆ pc ([0, t]; x) ⊆ l1 ([0, t]; x). Üstəlik, b-ni x-nin kompakt olmayanlıq ölçüsü ilə, bc-ni c-nin ( ]; x).
最后更新： 2021-05-09
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