On regularization of right hand sides of differential relations

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SynopsisLet the values ofFbe convex compact subsets ofRnand letFbe upper semicontinuous with respect tox. There are two ways known of replacingFby a more regular map so that the set of solutions of (2) remains unchanged. We prove that both ways lead to the same more regular map and extend the results to the case whereRnis replaced by a separable Banach space.