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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, Number 12, Pages 54–58 (Mi ivm8405)  
On an extreme point conjecture for concave functions

S. Ponnusamya, K.-J. Wirthsb

a Department of Mathematics, Indian Institute of Technology of Madras, Сhennai, India
b Institut für Analysis, Technical University of Braunschweig, Braunschweig, Germany
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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.
Received: 12.11.2010
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, Volume 55, Issue 12, Pages 44–47
DOI: https://doi.org/10.3103/S1066369X11120061
Bibliographic databases:
Document Type: Article
UDC: 517.546
Language: Russian
Citation: S. Ponnusamy, K.-J. Wirths, “On an extreme point conjecture for concave functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 12, 54–58; Russian Math. (Iz. VUZ), 55:12 (2011), 44–47
Citation in format AMSBIB
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\paper On an extreme point conjecture for concave functions
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
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\issue 12
\pages 54--58
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\transl
\jour Russian Math. (Iz. VUZ)
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\vol 55
\issue 12
\pages 44--47
\crossref{https://doi.org/10.3103/S1066369X11120061}
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