Meromorphic starlike functions with two fixed points (Q1096741)

If \(f(z)=a_ 0/z+\sum^{\infty}_{n=1}a_ nz\) n, \(a_ n\geq 0\), \(n\in {\mathbb{N}}\) is starlike of order \(\alpha\), i.e. if \(Re(zf'/f(z))<-\alpha\) for \(z\in {\mathbb{D}}=\{z| | z| <1\}\) then \[ \sum^{\infty}_{n=1}(n+\alpha)a_ n\leq a_ 0(1-\alpha), \] and conversely. Furthermore the authors study starlike meromorphic functions for which either \[ z_ 0f(z_ 0)=1 \] or \[ -z^ 2_ 0f'(z_ 0)=1 \] for some \(z_ 0\in]-1,1[\setminus \{0\}\), and give similar results for those functions.