Some simple criteria of starlikeness for meromorphic functions

In this paper we will use the theory of dierential subordinations to obtain a new condition for meromorphic functions, defined in the punctured disc ˙ U = U n f0g, U = fz 2C : jzj < 1g, which are of the form f(z) = 1 + anz n + an+1z n+1 + :::, to be starlike functions. The new condition for starlikeness is expressed by means of j(1 i fi)zf(z) + z 2 f 0 (z) + fij, where fi 2 [0;1).