The Growth Theorems And Distortion Theorems Of Spirallike Mappings

Spirallike mappings are more extensive than starlike mappings. In this thesis, westudy the growth and distortion theorems for spirallike mappings in a new way from anew perspective, which further improve the geometric function theory. The thesis consistsof three chapters.In the frst chapter,we briefy introduce some notations, defnitions, and the mainresults of this thesis.In the second chapter, we obtain the distortion theorems and the refning distortiontheorems for spirallike mappings of type β along a unit direction on the unit polydisc inC~n. And further, we give out the upper bound for them on the unit ball of a complexBanach space.In the third chapter, we use the parameter representation theory to research spirallikemappings in B_p space. Moreover, we gain the growth theorem,1/4covering theoremand distortion theorem.