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Let  h be a nonvanishing analytic function in the open unit disc with  h 0 = 1 . Consider the class consisting of normalized analytic functions  f whose ratios  f z / g z ,  g z / z p z , and  p z are each subordinate to  h for some analytic functions  g and  p . The radius of starlikeness of order  α is obtained for this class when  h is chosen to be either  h z = 1 + z or  h z = e z . Further, starlikeness radii are also obtained for each of these two classes, which include the radius of Janowski starlikeness, and the radius of parabolic starlikeness.

Starlikeness of Analytic Functions with Subordinate Ratios