Some Properties Of Two Subclasses Of Holomorphic Mappings

In this thesis, we study two classes of holomorphic mappings in several complex vari-ables, and obtain the estimations of some order item coe?cients of homogeneous expansionfor starlike mappings of orderα, quasi-convex mappings of orderα, and the growth andcovering theorems of quasi-convex mappings of orderαon bounded convex circular do-mains.The whole thesis consists of three chapters. In the first chapter, we introduce somedefinitions, notations and the main results of this thesis brie?y. In chapter 2, with theproperties of Loewner chains, the upper bound of the second order item coe?cients ofhomogeneous expansion for starlike mappings of orderαare obtained ; In chapter 3,first,considering the order zero (i.e.the origin 0 is a zero of order k+1 of a mapping f(x)?x), we generalize the upper bound of the second order item coe?cients to the upperbound from k +1 to 2k order item coe?cients of homogeneous expansion for quasi-convexmappings of orderα; second, the growth and covering theorems for the quasi-convexmappings of orderαare obtained.