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On successive coefficients of odd univalent functions
Author(s):
Zhongqiu
Ye
Journal:
Proc. Amer. Math. Soc.
133
(2005),
3355-3360.
MSC (2000):
Primary 30C45
Posted:
May 9, 2005
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Abstract:
The relative growth of successive coefficients of odd univalent functions is investigated. We prove that a conjecture of Hayman is true.
References:
-
- 1.
- G.M. Goluzin, Geometric Theory of Functions of a Complex Variable, Moscow, 1952.
- 2.
- W.K. Hayman, On successive Coefficients of Univalent Functions, J. London. Math. Soc. 38 (1963), 228-243. MR 0148885 (26:6382)
- 3.
- K.W. Lucas, On Successive Coefficients of Areally Mean-p valent Functions, J. London. Math. Soc, 44 (1969), 631-642. MR 0243055 (39:4379)
- 4.
- Hu Ke, On Succcessive Coefficients of Univalent Functions, Proc. Amer. Math. Soc. 95 (1986), 37-41. MR 0796442 (86j:30022)
- 5.
- I.M. Milin, Univalent Functions and Orthonomal System (Russian) Moscow, 1971.
- 6.
- V.I. Milin, Adjacent Coefficients of Odd Univalent Functions, Sib. Math. Journal 22 (1981), no. 2, 283-290. MR 0610775 (82i:30027)
- 7.
- Ch. Pommerenke, Univalent Functions, Vandenhoeck & Ruprecht, Göttingen, 1975. MR 0507768 (58:22526)
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Additional Information:
Zhongqiu
Ye
Affiliation:
Department of Mathematics, Jiangxi Normal University, Nanchang 330027, People's Republic of China
Email:
yezhqi@sina.com
DOI:
10.1090/S0002-9939-05-07922-0
PII:
S 0002-9939(05)07922-0
Keywords:
Successive coefficients,
univalent functions
Received by editor(s):
August 23, 2002
Received by editor(s) in revised form:
June 24, 2004
Posted:
May 9, 2005
Communicated by:
Juha M. Heinonen
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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