Abstract:
It is proved that in the space of Bochner-integrable mappings a multivalued mapping with nonconvex images has a continuous branch that, for a given single-valued mapping and for a previously specified accuracy, realizes the distance between the images of the single-valued mapping and the multivalued mapping. This result is applied to the investigation of properties of solutions of functional-differential inclusions with nonconvex right-hand side.
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