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 star-likeness, Math. Nachr. 248-249 (2003) 200-203] for the analytic functions to be in the class L* [1+Az/1+Bz] and its subclasses, where -1 <= B <= A <= 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 Lx-starlike functions. In this paper we give a generalization of main theorem contained in Tuneski (2003). Some applications involving this result are also considered. (C) 2007 Elsevier Inc. All rights reserved.