The Properties Of Some Classes Of Analytic Functions

This paper discusses the problem on the generalization of two classes of functions in complex analysis, which are defined in the open unit disc D={z:|z|<1}.This paper is composed of four parts.The first chapter in the paper is preface and preliminary knowledge. We briefly introduce some fundamental definitions and notations of this paper, and the research background of this paper.In the second part of this paper, we introduced a new class of analytic functions R(a).As a generalized class of univalent function, we studied the Hankel determinant:|a2a4-a32|of it and obtained a sharp upper bound for the functional|a2a4-a32|for f=R(a).In third chapter of this paper,tow new classes of functions are introduced by using subordinate.Those tow classes of analytic functions are S(u) and S(A, B). By study in these classes,the coefficient estimates of them are obtained and a rigorous proof is given.Finally,The fourth chapter of the paper is summarized and prospect.The principal results of this thesis succeed to the known results,and we extend them deep-ly and systematically. Owing to our research work, we have a further realization about the properties of subclasses of univalent function.