Kodai Mathematical Journal
- Kodai Math. J.
- Volume 30, Number 3 (2007), 385-393.
Domains of variability of Laurent coefficients and the convex hull for the family of concave univalent functions
Let D denote the open unit disc and let p (0,1). We consider the family Co(p) of functions f : D → that satisfy the following conditions:
(i) f is meromorphic in D and has a simple pole at the point p.
(ii) f(0) = f′(0) – 1 = 0.
(iii) f maps D conformally onto a set whose complement with respect to is convex.
We determine the exact domains of variability of some coefficients an (f) of the Laurent expansion
|z – p|<1 – p,
for f Co(p) and certain values of p. Knowledge on these Laurent coefficients is used to disprove a conjecture of the third author on the closed convex hull of Co(p) for certain values of p.
Kodai Math. J., Volume 30, Number 3 (2007), 385-393.
First available in Project Euclid: 1 November 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Bhowmik, Bappaditya; Ponnusamy, Saminathan; Wirths, Karl-Joachim. Domains of variability of Laurent coefficients and the convex hull for the family of concave univalent functions. Kodai Math. J. 30 (2007), no. 3, 385--393. doi:10.2996/kmj/1193924942. https://projecteuclid.org/euclid.kmj/1193924942