Many authors studied families XG of complex valued functions, which are holomorphic in bounded complete n-circular domains G⊂Cn and fulfill some geometric conditions. The above functions were applied later to research families of locally biholomorphic mappings in Cn. In this paper we consider a problem of inclusions between a few of such families XG and families MKG, k=2, 3, …, which are defined by applying a function decomposition with respect to the group of kth roots of unity.
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Let V be a closed convex cone and Cv be a space of nonempty closed convex subsets of a Banach space such that their Hausdorff distance form the cone V is finite. In this paper we embed the space Cv isometrically and isomorphically into a Banach space.
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