Radii of Starlikeness of Ratios of Analytic Functions with Fixed Second Coefficients

We introduce three classes of analytic functions with fixed second coefficients that are defined using the class P of analytic functions with positive real parts. The objective of this paper is to determine the radii such that the three classes are contained in various subclasses of starlike functions. The radii estimated in the present investigation are better than the radii obtained earlier. Furthermore, connections with previously known results are shown.