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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On a conjecture of D. Styer regarding univalent geometric and annular starlike functions


Authors: D. Bshouty and A. Lyzzaik
Journal: Proc. Amer. Math. Soc. 133 (2005), 1485-1490
MSC (2000): Primary 30C45
Published electronically: December 6, 2004
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Abstract: The aim of this paper is two-fold. First, to give a direct proof for the already established result of Styer which states that a univalent geometrically starlike function $f$ is a univalent annular starlike function if $f$ is bounded. Second, to show that the boundedness condition of $f$ is necessary, thus disproving a conjecture of Styer.


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Additional Information

D. Bshouty
Affiliation: Department of Mathematics, Technion, Haifa 32000, Israel
Email: daoud@tx.technion.ac.il

A. Lyzzaik
Affiliation: Department of Mathematics, American University of Beirut, Beirut, Lebanon
Email: lyzzaik@aub.edu.lb

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07674-9
PII: S 0002-9939(04)07674-9
Keywords: Univalent functions, starlike functions
Received by editor(s): September 30, 2003
Received by editor(s) in revised form: February 4, 2004
Published electronically: December 6, 2004
Additional Notes: The first author thanks the Promotion of Research Fund at the Technion for its support.
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.