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An estimate for certain meromorphic univalent functions


Author: Ming Qin Xie
Journal: Proc. Amer. Math. Soc. 102 (1988), 278-282
MSC: Primary 30C50,; Secondary 30C45
DOI: https://doi.org/10.1090/S0002-9939-1988-0920986-0
MathSciNet review: 920986
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Abstract: In this paper the coefficient problem for the family of univalent functions

$\displaystyle g\left( z \right) = z + \sum\limits_{n = 1}^\infty {{b_n}{z^{ - n}}} $

in $ \{ \left\vert z \right\vert > 1\} $ has been studied. The author obtained the sharp estimate $ {b_7} \leq 1/4 + 3/280$ when $ g(z)$ is an odd function and all its coefficients are real.

References [Enhancements On Off] (What's this?)

  • [1] P. R. Garabedian and M. Schiffer, A coefficient inequality for schlicht functions, Ann. of Math. (2) 61 (1955), 116-136. MR 0066457 (16:579c)
  • [2] Y. Kubota, A coefficient inequality for certain meromorphic univalent functions, Kodai Math. Sem. Rep. 26 (1974), 85-94. MR 0369683 (51:5915)
  • [3] H. A. [ill], [ill] [ill] [ill] [ill] [ill] [ill], "Nauka", Moscow, 1975, pp. 86-88.
  • [4] L. V. Ahlfors, Conformal invariants, McGraw-Hill, 1972, pp. 86-87.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0920986-0
Keywords: Univalent, coefficient, trajectory, quadratic differential
Article copyright: © Copyright 1988 American Mathematical Society

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