Properties Of Some Holomorphic Mappings On Bounded Balanced Domains

Starlike mappings and convex mappings are the main research contents of several complex geometric function theory,and the spirallike mappings containings both as a broader mappings class.In this paper,we will study the properties of spirallike mappings and their classes on bounded balanced domains by using the results of spirallike mappings on the unit ball in Cn,the properties of Loewner chains and the existing results on simple complex variable.In the first chapter,this paper briefly introduces the latest research background,basic concepts and main results of the theory of geometric functions with variables complex variables.In the second chapter,the conclusion related to spirallike mappings on unit ball Bn in Cn is extended to bounded balanced domain in Cn,and the coefficients or correlation terms of spirallike mappings are estimated.At the same time,we also study the properties of special mappings classes,such as a type spirallike mappings and starlike mappings in bounded balanced domains.