On an extreme point conjecture for concave functions

S. Ponnusamy^a, K.-J. Wirths<sup>b

a</sup> Department of Mathematics, Indian Institute of Technology of Madras, Сhennai, India
^b Institut für Analysis, Technical University of Braunschweig, Braunschweig, Germany

Abstract: Let $\mathrm{CO}(A)$, $A\in(1,2]$, denote the family of concave univalent functions in the unit disk $\mathbb D$ with opening angle at infinity bounded by $\pi A$. We prove a weak form of a conjecture on the extreme points of $\mathrm{clco\,CO}(A)$ from the paper in Indian J. Math. 50, 339–349 (2008).

Keywords: concave univalent functions, starlike functions, extreme points.

UDC: 517.546

Received: 12.11.2010

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:12, 44–47

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