Some Properties Research On Subclasses Of Biholomorphic Mappings In The Geometric Function Theory Of Several Complex Variables

This thesis is investigate the Fekete and Szego problem and corresponding problem for the subclass of starlike mappings of order α.This paper is composed of three chapters.In chapter one,we briefly introduce some definitions and notations and the research status in this thesis.In chapter two,we investigate the corresponding problem for the subclass of starlike mappings of order α defined on the unit ball in a complex Banach space,on the unit polydisk in Cn and the bounded starlike circular domain in Cn,respectively.In chapter three.we set Hk(Bn,Bn)be the set of all holomorphic mappings f from Bn into Bn such that z=0 is a zero of order k of f(z).In this paper,we research the boundary Schwarz lemma for this holomorphic mapping of k order zero on Bn in Cn.The main result of this thesis is extend some known results and further knowl-edge for the several complex variables geometric function theory.