Regular measures of noncompactness and Ascoli–Arzelà type compactness criteria in spaces of vector-valued functions

Abstract In this paper we estimate the Kuratowski and Hausdorff measures of noncompactness bounded subsets spaces vector-valued functions differentiable functions. To end, use a quantitative characteristic modeled on new equicontinuity-type concept classical characteristics related to pointwise relative compactness. We obtain regular in taken into consideration. The established inequalities reduce precise formulas some classes subsets. derive Ascoli–Arzelà type compactness criteria.