The Fekete-Szeg(?)inequality And Corresponding Problems For Subclasses Of Holomorphic Mappings In Several Complex Variables

This thesis is concerned with the Fekete and Szeg(?) problem for the class of normalized starlike mappings of order a and boundary Schwarz lemma for the holo-morphic mappings between unit balls in any dimensions.This paper is composed of three chapters.In chapter one,we briefly introduce the research status and 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 the unit ball in a complex Banach space or on the unit polydisk in Cn.In chapter three,we set Hm(Bn,BN)be the set of all holomorphic mappings f from Bn into BN such that z = 0 is a zero of order m of f(z).In this paper,we give the boundary Schwarz lemma for this mapping.The main result of this thesis is extend some known results and further knowl-edge for the several complex variables theory.