Some Subclasses Of Analytic Functions

In recent years,many scholars have studied new function classes and explored their related properties.In 1999,Silverman[22]defined the class Gb and investigated the inclusion relationship for Gb.And then Obradovic and Tuneski[19,25]improved the results proved by Silverman.In 1993,Mocanu[11]introduced the class M(?),In 2015,Nunokawa[18]considered the class M(?,?)which improved the class M(?),and he studied the order of strongly starlikeness in the class of M(?,?).Specially,M(?,1)?M(?).In 1973,Janowski defined the subordination by Schwarz function and used subordination to introduce a series of classes of analytic functions.Many scholars started to consider other new classes defined by subordination and investigated some properties of these classes.In 2016,Aouf,Mostafa and Zayed[2]introduced two subclasses of meromorphic functions and obtained convolution properties,confficient estimates and inclusion relationship for these subclasses.In 2017,H.M.Srivastava,P.Sharma and R.K.Raina[24]considered inclusion relationship for some interesting classes of analytic functions associated with a new fractional differntegral operator.Motivated by the above research,we define M(?,?,?),S?,H?1[?;A,B],K?,H?1[?;A,B],?Sv(?,?),?Cv(?,?,?)and ?Rv(?,?,?,?)according to the theory of Dziok-Srivastava linear operator,Bessel operator,starlike function and convex function,then explore some relevant properties of them.There are two main parts in this paper:The first part introduces the concept of starlike function,convex function,strongly starlike function,subordination,Hadamard convolution,Dziok-Srivastava linear operator,Bessel operator,etc,and some relevant lemmas which are used in this paper,then introduces some certain subclasses.The second part detaily discusses several properties of these subclasses,such as order of Strongly starlikeness,convolution properties,coefficient estimates,inclusion relationship,etc.