The Properties For Certain Subfamilies Of Univalent Functions

In this thesis,the properties of several classes of analytic function families and the coefficient estimation are studied.This thesis is composed of five parts.The first part is the introduction,which mainly introduces the research background and research status.The second part is the preliminary data,some important symbols,basic concepts and important properties of univalent function are introduced.In the third part,three new classes ?,C'U(?)are defined and their various properties are studied by convex and starlike functions,which includes radius of univalent,growth theorem,distortion theorem,convolution and the Fekete-Szego problem and so on.The fourth part is about coefficient estimation,which the coefficients |a2|,|a3| for certain subclasses of bi-univalent functions,and the radius of univalent of the n-th partial.The fifth part is the conclusion.In this part,we summarize our results.