Ma-Minda starlikeness of certain analytic functions

A normalized analytic function defined on the open unit disc D is called Ma-Minda starlike if z f'(z)/f (z) is subordinate to the function phi. For a normalized convex function f defined on D and alpha > 0, we determine the radius of Ma-Minda starlikeness of the function g defined as g(z) = (z f'(z)/f (z))(alpha) f (z) for certain choices of phi. In particular, we investigate the radius of Janowski starlikeness of the function g.