Applications of a decomposition of holomorphic mappings in Cn with respect to a cyclic group

In the paper the decomposition with respect to the group of roots of unity is applied to characterize some classes of biholomorphic mappings in Cn. There is considered the problem of subordination and majorization relations between convex mappings and their components in the above partition. There is also given a distortion theorem for convex mappings and a criterion for starlikeness in Cn.  2003 Elsevier Science (USA). All rights reserved