Starlikeness of the Libera transform of functions with bounded turning

Conditions are determined for starlikeness of the Libera transform of functions with bounded turning. The results of Miller and Mocanu [S.S. Miller, P.T. Mocanu, Libera transform of functions with bounded turning, J. Math. Anal. Appl. 276 (2002) 90-97] are improved by using the theory of differential subordinations.