Uniformly Starlike Mappings And Uniformly Convex Mappings On The Unit Polydisc In C~n

In this thesis, we study the uniformly starlike mappings and uniformly convex map-pings on the unit polydisc inCn. The whole thesis contains three chapters.In the first chapter, we introduce the background of this thesis, some notations anddefinitions, and the main results of this thesis briefly.In the second chapter, we give the definition and criterion of the uniformly starlikemappings on the unit polydisc inCn, and obtain some estimates of inequalities.In the last chapter, we discuss the uniformly convex mappings on the unit polydiscinCn, give the definition and criterion of the uniformly convex mappings, and obtain aresult which is similar to Harnack inequality.