On some problems of James Miller

We consider the class of meromorphic univalent functions having a simple pole at $p\in(0,1)$ and that map the unit disc onto the exterior of a domain which is starlike with respect to a point $w_0 \neq 0,\, \infty$. We denote this class of functions by $Σ^*(p,w_0)$. In this paper, we find the exact region of variability for the second Taylor coefficient for functions in $Σ^*(p,w_0)$. In view of this result we rectify some results of James Miller.

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