Certain subclasses of meromorphic harmonic starlike functions

Abstract

In a previous paper M.- P. Chen, Z.- R. Wu and Z.- Z. Zou [ M. P. Chen, Z.- R. Wu and Z.- Z. Zou, On functions alpha- starlike with respect to symmetric conjugate points, J. Math. Anal. Appl. 201 ( 1996) 25 - 34] developed a method, using some operators, to deal with functions analytic and starlike with respect to symmetric conjugate points in the unit disc. In this paper, we employ this method to functions meromorphic harmonic in (U) over tilde = {z:vertical bar z vertical bar > 1}. Especially, a sharp coefficient estimate and a structure representation of such functions are obtained.