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