On a class of univalent functions

Abstract

We consider the class of univalent functions f(z)=z+a3z3+a4z4+⋯ analytic in the unit disc and satisfying |(z2f′(z)/f2(z))−1|<1, and show that such functions are starlike if they satisfy |(z2f′(z)/f2(z))−1|<(1/2).