Properties Of Some Subclasses Of Univalent Functions

The thesis is divided into four parts.The first part is the introduction.It mainly introduces the relevant research context and current status of univalent function theory.The major theorems and conclusions of subfamilies of univalent functions are also reviewed.In the second part,the function family C₁（0,λ） is defined,and its properties are studied,which include growth theorem,distortion theorem,the upper bounds of the absolute value of the difference between adjacent Taylor coefficients,convolution and Fekete-Szeg（?） problem.Then two new families of functions （?）（β,λ） and K^*（β,λ）are defined and their properties are got,which include growth theorem,distortion theorem,coefficient estimates and so on.In the third part,the definition of function family M is defined and we studied the logarithmic coefficients,the upper bounds of the moduli on the second order Hankel determinants H₂（2）,the third order Toeplitz determinants T₃（1）of these subclasses and so on.The fourth part sums up the result of the full text.