New results related to the starlikeness of Bernardi integral operator

Abstract

In Lewandowski, Miller and Zlotkiewicz, Generating functions for some classes of univalent functions, Proc. Amer. Math. Soc., 56 (1976), pp. 111–117 and Pascu, Alpha-close-to-convex functions, Romanian Finish Seminar on Complex Analysis, Springer, Berlin, 1979, pp. 331–335 it has been proved that the integral operator defined by Bernardi in Convex and starlike univalent functions, Trans. Amer. Math. Soc., 135 (1969), pp. 429–446 given by preserves certain classes of univalent functions such as the class of starlike functions, the class of convex functions and the class of close-to-convex functions. In this article, we determine conditions that a function f ∈ A needs to satisfy such that the function F given by (1) is starlike.