Bhowmik, Bappaditya (2010) On some results of A. E. Livingston and coefficient problems for concave univalent functions. In: Archiv der Mathematik, 95 (6). pp. 575-581.
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We consider functions that map the open unit disc conformally onto the complement of a bounded convex set. We call these functions concave univalent functions. In 1994, Livingston presented a characterization for these functions. In this paper, we observe that there is a minor flaw with this characterization. We obtain certain sharp estimates and the exact set of variability involving Laurent and Taylor coefficients for concave functions. We also present the exact set of variability of the linear combination of certain successive Taylor coefficients of concave functions.
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to Springer.|
|Keywords:||Concave univalent functions;Taylor and Laurent coefficients.|
|Department/Centre:||Division of Physical & Mathematical Sciences > Mathematics|
|Date Deposited:||07 Feb 2011 12:22|
|Last Modified:||07 Feb 2011 12:22|
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