On concave univalent functions

Bhowmik, Bappaditya (2012) On concave univalent functions. In: Mathematische Nachrichten, 285 (5-6). pp. 606-612.

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Abstract

We consider functions that map the open unit disc conformally onto the complement of an unbounded convex set with opening angle pa, a ? (1, 2], at infinity. In this paper, we show that every such function is close-to-convex of order (a - 1) and is included in the set of univalent functions of bounded boundary rotation. Many interesting consequences of this result are obtained. We also determine the extreme points of the set of concave functions with respect to the linear structure of the Hornich space.

Item Type:	Journal Article
Publication:	Mathematische Nachrichten
Publisher:	John Wiley and Sons
Additional Information:	Copyright of this article belongs to John Wiley and Sons.
Keywords:	Concave univalent functions;Taylor and Laurent coefficients; MSC (2010) 30C45
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	01 May 2012 10:38
Last Modified:	10 May 2012 04:51
URI:	http://eprints.iisc.ac.in/id/eprint/44340

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