The Parametric Representation Of A Class Of Spirallike Mappings In The Banach Space

The spirallike mapping is a main research object in the geometric function theoryof several complex variables. Spirallike mapping of order α is a special class of spirallikemapping. In this paper, we deal with the spirallike mapping of order α in the unit ballof Banach space. And we will study some properties of the spirallike mapping of order αincluding the growth theorem. The whole thesis contains three chapters.In the first chapter, we introduce briefly the background of the development of thegeometric function theory of several complex variables, some notations, basic concepts,some lemmas and the main results of the thesis.In the second chapter, we get the parametric representation of the spirallike mappingof order α in the unit ball B of Banach space.In the third chapter, through the front of research learning, we get the growth theoremand a description of the spirallike mapping of order α.