On meromorphically harmonic starlike functions with respect to symmetric conjugate points (Q864699)

In a previous paper \textit{M. P. Chen, Z.-R. Wu} and \textit{Z.-Z. Zou} [J. Math. Anal. Appl. 2001, 25--34 (1996; Zbl 0853.30008)] developed a method, using some operators, to deal with functions holomorphic and starlike with respect to symmetric conjugate points in the unit disc \(U:= \{z:z\in\mathbb{C}\}\). Next, the same method is employed to functions meromorphic in \(U\) by \textit{Z. Z. Zou} and \textit{Z.-R. Wu} [J. Math. Anal. Appl. 261, No. 1, 17--27 (2001; Zbl 0993.30007)]. In this paper the method is employed to functions meromorphic harmonic in the punctured disc \(U\setminus\{0\}\). Let \(\mathbb{M}\mathbb{H}\) denote the class of functions \(f\) of the form \[ f(z)=h(z)+\overline{g(z)}=\frac 1z+ \sum^\infty_{n= 1}a_nz^n+\overline{\sum^\infty_{n=1}b_nz^n} \] which are univalent harmonic in the set \(U\setminus\{0\}\). The authors consider some subclasses of the class \(\mathbb{M} \mathbb{H}\), some properties of these classes such as coefficient estimates and a structural formula are obtained.