On the Refined Esitmates of All Homogeneous Expansions for a Subclass of Biholomorphic Starlike Mappings in Several Complex Variables

The refined estimates of all homogeneous expansions for a subclass of biholomorphic starlike mappings are mainly established on the unit ball in complex Banach spaces or the unit polydisk in ℂ n with a unified method. Especially the results are sharp if the above mappings are further k -fold symmetric starlike mappings or k -fold symmetric starlike mappings of order α . The obtained results unify and generalize the corresponding results in some prior literatures.