|
On a conjecture of D. Styer regarding univalent geometric and annular starlike functions
Author(s):
D.
Bshouty;
A.
Lyzzaik
Journal:
Proc. Amer. Math. Soc.
133
(2005),
1485-1490.
MSC (2000):
Primary 30C45
Posted:
December 6, 2004
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
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  is a univalent annular starlike function if  is bounded. Second, to show that the boundedness condition of  is necessary, thus disproving a conjecture of Styer.
References:
-
- 1.
- J. Bender, Some extremal theorems for multivalently star-like functions, Duke Math. J. 29 (1962), 101-106. MR 0132171 (24:A2018)
- 2.
- A. W. Goodman and E. B. Saff, On univalent functions convex in one direction, Proc. Amer. Math. Soc. 73 (1979), 183-187. MR 0516461 (80e:30006)
- 3.
- W. Hengartner and G. Schober, A remark on level curves for domains convex in one direction, Appl. Anaysis 3 (1973), 101-106. MR 0393450 (52:14260)
- 4.
- J. A. Hummel, Multivalent starlike functions, J. Analyse Math. 18 (1967), 133-160. MR 0209461 (35:359)
- 5.
- D. Styer, Geometric and annular starlike functions, Complex Variables 29 (1996), 189-191. MR 1382965 (97b:30021)
- 6.
- D. Styer, An analytic characterization of geometrically sta rlike functions, Michigan Math. J. 23 (1976), 137-139. MR 0409792 (53:13544)
- 7.
- Ch. Pommerenke, Univalent functions, Vandenhoeck & Ruprec ht, Göttingen, 1975. MR 0507768 (58:22526)
- 8.
- Ch. Pommerenke, Boundary behaviour of conformal maps, Springer-Verlag, Berlin, 1992. MR 1217706 (95b:30008)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
30C45
Retrieve articles in all Journals with MSC
(2000):
30C45
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:
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
Posted:
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 of article:
Copyright
2004,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
Comments: webmaster@ams.org