Some simple criteria of starlikeness for meromorphic functions

Abstract

In this paper we will use the theory of differential subordinations to obtain a new condition for meromorphic functions, defined in the punctured disc ? = U \ {0}, U = {z ? C : |z| < 1}, which are of the form f(z) = 1/2 + anzn + an+1zn+1 + ... , to be starlike functions. The new condition for starlikeness is expressed by means of |(1 - ?)zf(z) + z2 f'(z) + ?|, where ? ? [0, 1). .