Radius of Starlikeness of Certain Analytic Functions

This paper studies analytic functions $f$ defined on the open unit disk of the complex plane for which $f\mathrm{/}g$ and $(1+z)g\mathrm{/}z$ are both functions with positive real part for some analytic function $g$. We determine radius constants of these functions to belong to classes of strong starlike functions, starlike functions of order $\alpha$, parabolic starlike functions, as well as to the classes of starlike functions associated with lemniscate of Bernoulli, cardioid, lune, reverse lemniscate, sine function, exponential function and a particular rational function. The results obtained are sharp.