On some problems of James Miller

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

doi:10.4067/S0719-06462010000100003

Authors

B. Bhowmik Department of Mathematics, Indian Institute of Technology Madras, Chennai-600 036, India.
K.-J. Wirths Institut f¨ur Analysis, TU Braunschweig, 38106 Braunschweig, Germany.
S. Ponnusamy Department of Mathematics, Indian Institute of Technology Madras, Chennai-600 036, India.

DOI:

https://doi.org/10.4067/S0719-06462010000100003

Keywords:

Starlike, meromorphic, Schwarz‘ functions, Taylor coefficient

Abstract

We consider the class of meromorphic univalent functions having a simple pole at p âˆˆ (0, 1) and that map the unit disc onto the exterior of a domain which is starlike with respect to a point ð“Œ₀ â‰ 0, âˆž. We denote this class of functions by Î£^âˆ— (p, ð“Œ₀). In this paper, we find the exact region of variability for the second Taylor coefficient for functions in Î£^âˆ— (p, ð“Œ₀). In view of this result we rectify some results of James Miller.