On some problems of James Miller

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DOI:

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

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.

Keywords

Starlike , meromorphic , Schwarz‘ functions , Taylor coefficient
  • 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.
  • Pages: 15–21
  • Date Published: 2010-03-01
  • Vol. 12 No. 1 (2010): CUBO, A Mathematical Journal

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Published

2010-03-01

How to Cite

[1]
B. Bhowmik, K.-J. Wirths, and S. Ponnusamy, “On some problems of James Miller”, CUBO, vol. 12, no. 1, pp. 15–21, Mar. 2010.

Issue

Vol. 12 No. 1 (2010): CUBO, A Mathematical Journal

Section

Articles