An estimate for certain meromorphic univalent functions
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- Proc. Amer. Math. Soc. 102 (1988), 278-282 Request permission
Abstract:
In this paper the coefficient problem for the family of univalent functions \[ g\left ( z \right ) = z + \sum \limits _{n = 1}^\infty {{b_n}{z^{ - n}}} \] in $\{ \left | z \right | > 1\}$ 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
- P. R. Garabedian and M. Schiffer, A coefficient inequality for schlicht functions, Ann. of Math. (2) 61 (1955), 116–136. MR 66457, DOI 10.2307/1969623
- Yoshihisa Kubota, A coefficient inequality for certain meromorphic univalent functions, K\B{o}dai Math. Sem. Rep. 26 (1974/75), 85–94. MR 369683 H. A. [ill], [ill] [ill] [ill] [ill] [ill] [ill], "Nauka", Moscow, 1975, pp. 86-88. L. V. Ahlfors, Conformal invariants, McGraw-Hill, 1972, pp. 86-87.
Additional Information
- © Copyright 1988 American Mathematical Society
- 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