On The Properties Of A Subclass Of Univalent Functions

In this paper,author investigates the properties of some subclasses of univalent functions.This paper is composed of five 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 main results of this paper.In second chapter of this paper,we introduce a subclass(?)_α^βof spiral-like functions of typeβand obtain its growth,covering theorems and the sharp bound for the second term coefficient estimate of functions in f(z)∈(?)_α^β.in particular,we give a important relation of functions between (?)_α^βand S^*(α).In third chapter of this paper,by using absolutely different way from that in the second chapter we get more refined growth,covering theorems and the sharp bound for the n-th term coefficient estimate of functions in f(z)∈(?)_α^β.In fourth chapter of this paper,we mainly investigate the properties of a subclass S_p^*(α,β,γ) of starlike functions of orderα,including its coefficient estimate,distortion theorem,closure theorem and extreme points theorem.In the fifth chapter of this paper,by using convolution techniques,we investigate theδ-neighborhoods of a subclass R^b(h) and R^b'(h) of univalent functions.The main significance of this thesis lies in extending or improving some known results. in particular,we reveal the essential relation of the properties of a subclass of univalent functions. Therefore,we have a deep realization about the properties of a subclass of univalent functions.