On a subclass of strongly starlike functions

Let S ∗ ( q c ) , c ∈ ( 0 , 1 ] , denote the class of analytic functions f in the unit disc U normalized by f ( 0 ) = f ′ ( 0 ) − 1 = 0 and satisfying the condition | [ z f ′ ( z ) / f ( z ) ] 2 − 1 | ∣ < c , z ∈ U . The relations between S ∗ ( q c ) and other classes geometrically defined are considered. The radii of convexity (starlikeness) of order α are calculated. The same problem in the class of strongly starlike functions of order β is also considered.