On The Study Of The Properties Of Subclasses Of Univalent Function By A Unified Way

In the paper,we study the subclasses of univalent function by the unified way. This paper is composed of four parts.The first chapter in the paper is preface and preliminary knowledge. We introduce our achievement on univalent function, the definition , the meaning of symbols, and a important lemma.In the second chapter, we define a subclass function M g( n,λ, b), which contains extensive representative,concludes many classic subclasses, such as S *(b ),C (b ),S* (1 -β),C (1 -β),D ( n,λ, b), B ( n,λ,α, b), and so on. At the same time, We get the coefficients' estimate of M g( n,λ, b), the result generalize many known results.In the third chapter, we study an important subclasses of univalent function, it is a subclass of starlike functions with respect to symmetric points (In third chapter, definition, Ss? ,S s? ( A, B),K s? ( A, B),and so on) , then, we generalize the essential features, and define two subclasses S s? ( g),K s? ( g), afterwards, we obtain the coefficients' estimate of them, the result generalize many known results.In the last chapter, we introduce a subclass of univalent function, and obtain the coefficients' estimate, the result extend some know results.The main significance of this thesis lies in extending and unifying the know results. In general, we show the essential links, so we renew the knowledge which contain the properties and contacts of many subclasses on univalent function.