On the multivalence and order of starlikeness of a class of meromorphic functions |
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Authors: | Zalman Rubinstein Dorothy Browne Shaffer |
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Affiliation: | (1) University of Haifa, Haifa, Israel;(2) Fairfield University, Fairfield, Connecticut, USA |
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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/z p 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. |
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