Properties Of Some Multivalent Analytic Function Classes

Throughout the development of geometric function theory,the combination of linear operator and differential dependency is an important tool for research.It has been widely used in the study of complex differential equations,meromorphic functions,harmonic functions,Banach Spaces,convolution theory and so on.In recent years,many scholars have defined many different classes of functions by using differential dependency and linear operators,and studied the related properties of these new classes of functions.In 2003,J.Dziok and H.M.Srivastava used Montel normalization to study the coefficient estimation,deviation theorem,convex radius and starness radius of a specific subclass of analytic funcitons.In 2007,J.Patel,A.K.Mishra and H.M.Srivastava studied the inclusion relations of the class of multivalent analytic functions of Dziok-Srivastava operators,the real part estimation,the module estimation,the argument estimation of the operator,the sufficient conditions for functions to belong to the class of functions and the generalized neighborhood of the class of functions.In 2009,M.K.Ouf and H.E.Darwiah studied the deviation theorem,extreme point,coefficient estimation,convex radius and nearly convex radius,and modified Hadamard convolution for the class of multivalent analytic functions.In 2017,J.L.Liu and H.M.Sivastava investigated the inclusion relations,integral representations,and convolution properties of subclasses of some multivalent analytic functions.The purpose of this paper is to define some classes of multivalent analytic functions by using linear operators related to analytic functions and differential dependency theory,and to explore the properties of functions in classes.This paper is made up of four chapters.The first chapter is the introduction and preliminary knowledge,which introduces the research of this thesis.We also studies on the promotion of some new classes such as SLp?STp(?)?CVp(?)?Sp?CSp(?)?Mp(?)on the basis of previous,and defines the class?p(k,c,?;h)by using differential dependency.In the second chapter,we define the class SL(p)of multivalate analytic functions related to the lemniscate of Bernoulli.By using the theory of differential dependency,we give some sufficient conditions for the functions in class SLp and class SL(p).In Chapter 3,we discuss the radius of starlikeness related to the lemniscate of Bernoulli for functions of class STp(?)and class CVp(?),namely SLp-radius,and radius related to class Mp(?),namely Mp(?)-radius.In Chapter 4,the convolution and starlikeness radius of class ?p(k,c,?;h)are obtained by using the method of combining the related operator Tk,c of Bessel function Jv((?))on the unit disk with the theory of differential dependency.