星象函数及其导数的凸组合的星象半径

Radius of Starlikeness for Certain Combination ofStarlike Functions and Their Derivatives

设F(z)=z+…是|z|＜1上的ρ级星象函数,0≤ρ＜1.本文确定了 f(z)=(1-λ)F(z)+λF(z) 的ρ级星象半径,其中λ>0.

Let F(z)=z+…be starlike of order ρ, 0≤ρ<l, in |z|<l. We determine the radius of starlikeness of order ρfor the class of functions f(z) = (l-λ)F(z)+λzF'(z),whereλ≥0.