The Generation Of Fekete-Szeg? Inequality And Schwarz-pick Lemma In One Complex To Several Complex Variables

This thesis is concerned with the Fekete and Szeg? problem and Schwarz-Pick lemma for the holomorphic mappings f from 1D into BP.This paper is composed with three chapters.In chapter one,we briefly introduce the developmental background of holomor-phic function,and some definitions,notations in this thesis.In chapter two,first,we establish the Fekete-Szeg? inequality for the subclass of S?*Second,we generalize this result to the unit ball in Banach complex spaces and the unit poly disc in Cn.In chapter three,we defined an interesting holomophic mappings f from D into BP.Then,we give the Schwarz-Pick lemma and the precision for the modulus of this family.And extend the two important results to the several complex variable,we improve the original method and make a futher promotion in depth.