On sufficient condition to be in a certain subclass of starlike functions defined by subordination

An interesting criterion was given by Tuneski [N. Tuneski, On the quotient of the representations of convexity and starlikeness, Math. Nachr. 248–249 (2003) 200–203] for the analytic functions to be in the class S 1⁄21þAz 1þBz and its subclasses, where 1 6 B < A 6 1. This result is an extension of an earlier result of Silverman [H. Silverman, Convex and starlike criteria, Int. Math. Math. Sci. 22 (1) (1999) 75–79] for a-starlike functions. In this paper we give a generalization of main theorem contained in Tuneski (2003). Some applications involving this result are also considered. 2007 Elsevier Inc. All rights reserved.