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arXiv · 1008.5270

On some problems of James Miller

B. Bhowmik·S. Ponnusamy·K-J. Wirths
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Abstract

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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B. Bhowmik, S. Ponnusamy, K-J. Wirths. 2010-08-31. On some problems of James Miller. https://arxiv.org/abs/1008.5270

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