On the order of strongly starlikeness in some classes of starlike functions

We consider the order of strongly starlikeness in the class of analytic functions f, f(0) = 0, f' (0) = 1, such that $$\left|\frac{1 + zf^{\prime\prime}(z)/f^{\prime}(z)}{zf^{\prime}(z)/f(z)} - 1\right| < b \quad {\rm for} \quad z \in \mathbb{D}$$ . We consider also the same problem for α-convex functions of order β.