Radius of starlikeness of certain analytic functions

We investigate radius problems for three classes of normalized analytic functions f characterized by its ratio with certain normalized analytic functions g. The first two classes consist of functions f satisfying Re(f (z)/g(z)) > 0 with either Re(g(z)/s(z)) > 0 or Re(g(z)/s(z)) > 1/2 and the other class consists of functions f satisfying |(f (z)/g(z)) - 1| < 1 with Re(g(z)/s(z)) > 0 for some starlike function s of order a, 0 <= alpha < 1. For functions in these classes, we compute the various radii of starlikeness, including the radius of starlikeness of order alpha, and radius of Ma-Minda starlikeness associated with parabola, lemniscate of Bernoulli, exponential function, cardioid, sine, lune, rational function and nephroid.