On the multivalence and order of starlikeness of a class of meromorphic functions

Abstract

Basically this paper deals with the determination of the radius of starlikeness and radius of univalence of the class of meromorphic functions of the formg(z)=A/z−Φ(z) forA>0, and where Φ(z) is an analytic function defined in the unit disk whose modulus does not exceed unity. We estimate the radius ofp-valence of functions having the fromh(z)=Φ(z)+a/zp fora>1,p≧1, and also estimate the radius of starlikeness of certain Blaschke products which is also given as a function of the minimum modulus function. We discuss the question of sharpness of the results and mention some open problems.