A New Subclass Of Multi - Leaf Analytic Functions

Analytic functions has been a highly focused research object in recent years,scholars have most interests in discussing and exploring it,such as Luo,Zhang who made a series of discussions in analytic functions. At present, more researchers devote themselves to studying the new operator and searching their properties and various of properties of function classes.The objective of the present paper is to study new subclasses of multivalent function in the open unit disc U by multiplier transformation. From that, we can explore their multifarious properties, specially, we can acquire some inclusion relationships and some properties referred to integral operator. We use Hadamard product to define a new operator: and define new subclasses of analytic functions by using subordination technique: Investigating the inclusion relationships of Tpβ and some properties of Dpβ.This paper studies the properties of multivalent function by differential subordination, and it is divided into five chapters:The first chapter introduces the research status and understands varies discuss of analytic functions by a lot of recent scholars.The second chapter deals mainly with some concepts of subordination,convolution and so on. Apart from this, we define the new operator of Dpβ and new subclasses of Tpβ of functions.In the third chapter, we use some lemmas, which will be needed later in the fourth and fifth chapters.The fourth chapter deals with the inclusion relationships of Tpβ.In the fifth chapter,we introduce the properties which are related with Dpβ.