On some problems of James Miller

B. Bhowmik; S. Ponnusamy; K-J. Wirths

On some problems of James Miller

Complex Variables 2010-09-01 v1

Authors: B. Bhowmik , S. Ponnusamy , K-J. Wirths

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 $\Sigma^*(p,w_0)$ . In this paper, we find the exact region of variability for the second Taylor coefficient for functions in $\Sigma^*(p,w_0)$ . In view of this result we rectify some results of James Miller.

Keywords

univalent functions

Cite

@article{arxiv.1008.5270,
  title  = {On some problems of James Miller},
  author = {B. Bhowmik and S. Ponnusamy and K-J. Wirths},
  journal= {arXiv preprint arXiv:1008.5270},
  year   = {2010}
}

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