Radius Of Starlikess For A Certain Class Of Analytic Function

Let D={z:|z|<1} denote the unit disk , m denote positive integer andα∈[0,1). LetF_m(α)={f:f(z)=z+sum from n=1 to∞a_nz^mn+1 is analytic in D and Ref(z)/z>α}.This thesis focuses on the radius of starlikeness for F_m(α), that is, we find a commom r_m^*(α)∈(0,1) such that f(z) maps {z:|z|m^*(α)} onto the starlike image f(|z|m^*(α)) for any f(z)∈F_m(α), and that the r_m^*(α) can't be enlarged. This thesis consists of three Chapters. In Chapter 1, the background and the gained results are introduced and summarized. In Chapter 2, a new function class P_m(1-2α) which has close relationship with F_m(α) is studied. The best lower bound estimation of Rez(?)(z)/(p(z)) for p(z)∈P_m(1-2α) is given, and it also forms a basis for our further studying of the radius of starlikeness. In Chapter 3, by using the relationship of F_m(α) and P_m(1-2α) as well as the results got in Chapter 2, we gives the exact values of r_m^*(α) and the relational external funtions.