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 SLSL if zf′(z)/f(z) lies in the region bounded by the right-half of the lemniscate of Bernoulli given by ∣w2 − 1∣ < 1. In the present investigation, the SLSL-radii for certain well-known classes of functions are obtained. Radius problems associated with the left-half plane are also investigated for these classes.