The Properties Of A Class Of Univalent Functions

Let A be the classes of functions analytic in the unit disk D={z:|z|<1}.Let u de-note the set of all functions f ? A satisfying the conditions f(0)=f'(0)-1=0 and Let ?? denote the set of all functions f?A satisfying the conditions f(0)=f(0)-1=0 and|zf'(z)-f(z)|<?,0<??1/2,|z|<1.In this article,the properties of ?? are discussed,which include convexity radius,convolution,closed convex properties,support points and extreme points,etc.,and more general con-clusions are got.Then the relationship between U and ?? are studied and some new results are got from generalized Robinson's 1/2-Conjecture.Finally,the coefficients of ?? under different conditions are estimated,and more stringent estimation results are obtained than before.At the same time,the Fekete-Szego problem of its coefficients and the Libera integral operator on ?? are discussed,and general conclusions are obtained.