The Fekete-Szeg? Inequality Of Subclasses Of Starlike Mapping In Several Complex Variables And The Sharp Estimates Of Boundary Schwarz Lemma

This thesis is concerned with the Fekete and Szeg? problem for the class of nor-malized starlike mappings and Schwarz lemma for the holomorphic mappings with classics domain in the high dimensions.This paper is composed of three chapters.In chapter one,we briefly introduce the research history and status,give some definitions and notations in this thesis.In chapter two,we establish the Fekete-Szeg? inequality for the class of starlike functions in unit disk,and then we generalize this result to a subclass of the starlike mapping in the unit ball in a complex Banach space?the unit polydisk or the bounded starlike circular domain in Cn.In chapter three,we consider the classical holomorphic class which is Hk(X,Y)(we will define it in the chapter one),we get a kind of Schwarz-Pick lemma about Hk(Bn,BN)and the boundary Schwarz lemma about Hk(Dn,BN)?Hk(Bn,BN).The main result of this thesis is extend some known results and further knowl-edge for the several complex variables theory.