Radii of Starlikeness Associated with the Lemniscate of Bernoulli and   the Left-Half Plane
  A normalized analytic function f defined on the open unit disk in the complex plane is in the class SL if zf'(z)/f(z) lies in the region bounded by the right-half of the lemniscate of Bernoulli given by |w^2 - 1| < 1. In the present investigation, the SL-radii for certain well-known classes of functions are obtained. Radius problems associated with the left-half plane are also investigated for these classes 
Rosihan M. Ali, Naveen Jain, and V. Ravichandran
math.CV