The Properties Of Some Subclasses Of Univalent Functions

This thesis is concerned with some subclasses of univalent functions. This paper is composed of five chapters.In chapter one, we briefly introduce the developed background of univalent function, some definitions and notations in this thesis.In chapter two, using the geometric properties of starlike function of orderαand analysis depict of spiral-like function of typeβ, we define a new class of function S_α~βand obtain its properties of growth,covering theorem and coefficient estimate.In chapter three, considering the zero of order, we obtain more refined growth,covering theorem and sharp coefficient estimate of function (?).In chapter four, we study some properties of P-valent analytic functions with negative coefficients, including its coefficient estimate, distortion theorem, closure theorem and extreme points theorem.In the last chapter, we study a subclass TS(α,β) of close-to-convex functions and obtain its properties of coefficient inequalities.The principal results of this thesis succeed to the known results, and we extend them deeply and systematically. Owing to our research work, we have a further realization about the properties of subclasses of univalent functions.