The Parametric Representation Of Spiral-like Mapping With Respect To A In The Banach Space

Multi-complex geometric function mainly studies the nature of holomorphic mappings,and the spiral-like mapping is a kind of very wide range of holomorphic mappings.In this paper,the properties of spiral-like mapping on unit sphere of the Banach space are discussed,we deal with the parametric representation of spiral-likes mapping in the unit ball of the Banach space.As an application,we obtain the growth theorem of spiral-like mapping on B.The paper is divided into three chapters.In the first chapter,we recommend the background of the development of spiral-like mapping and some notations,basic concepts,some lemmas and some results.In the second chapter,the parametric representation of spiral-likes mapping is given in the Banach space.In the third chapter,using the parametric representation of spiral-like mappings,we obtain the growth theorem of a special kind of spiral-like mapping.