On a conjecture of D. Styer regarding univalent geometric and annular starlike functions
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- by D. Bshouty and A. Lyzzaik PDF
- Proc. Amer. Math. Soc. 133 (2005), 1485-1490 Request permission
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.References
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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
- MR Author ID: 117325
- Email: lyzzaik@aub.edu.lb
- 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
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 1485-1490
- MSC (2000): Primary 30C45
- DOI: https://doi.org/10.1090/S0002-9939-04-07674-9
- MathSciNet review: 2111949