Properties Of Several Classes Of Close-to-Convex Functions

The theory of univalent functions,also known as the theory of geometric functions,is an important branch of the theory of univalent complex functions.Function families U and the class of close-to-convex funcions have been widely studied in recent decades.This paper also studies these two types of function families based on the research of other scholars.The paper is mainly divided into four chapters,the specific contents are as follows:The first chapter introduces the research background and current situation of univalent function theory.The second chapter introduces some symbols,definitions and theorems needed in this paper.The third chapter introduces the U radius of two kinds of functions.In this chapter,this article defined two kinds of new functions based on the function classes studied by Rosihan and Najla,and make corresponding research.The fourth chapter introduces four classes of close-to-convex functions.First,the definitions of these four classes of function families are given,and their coefficients are discussed.The problems of Toeplitz determinant and Fekete-Szeg(?) are discussed under the condition of a2∈R.The fifth chapter makes a brief summary and prospect of the research content of this paper.