The Generation Of Two Important Results In One Complex To Higher Dimensions

This thesis is concerned with the Fekete and Szeg(?) problem in several complex variables and schwarz lemma for the of modulus of holomorphic mappings on D.this paper is composed with three chapters.In chapter one, we briefly introduce the developmental background of holomorphic function, and some definitions, notations in this thesie.In chapter two, we extend the well-know Fekete-Szeg(?) inequality in one variable to higher dimension space. That is, we establish the Fekete-Szeg(?) inequality for the class of starlike mappings defined on the bounded starlike circular domain in Cn.In chapter three, we set Hm(D, Bp) be the set of all holomophic mappings f from D into Bpsuch that z = 0 is a zero of order m of f(z)- f(0). In this chapter,we give the schwarz-pick lemma for the modulus of the function family.The work of this paper is extend two important results in one variable to several variables space, and further enriching the several complex variables theory.