On some problems of James Miller

Abstract

We consider the class of meromorphic univalent functions having a simple pole at p ∈ (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, ∞. We denote this class of functions by Σ^∗ (p, ð“Œ₀). In this paper, we find the exact region of variability for the second Taylor coefficient for functions in Σ^∗ (p, ð“Œ₀). In view of this result we rectify some results of James Miller.