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On coefficient inequalities for meromorphic univalent functions


Author: Li Quan Liu
Journal: Proc. Amer. Math. Soc. 114 (1992), 413-422
MSC: Primary 30C70; Secondary 30C75
DOI: https://doi.org/10.1090/S0002-9939-1992-1086333-2
Correction: Proc. Amer. Math. Soc. 120 (1994), null.
MathSciNet review: 1086333
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Abstract | References | Similar Articles | Additional Information

Abstract: We obtain some coefficient inequalities for the class $ \Sigma $ consisting of functions of the form $ f(z) = z + {b_0} + {b_1}/z + \cdots $ that are meromorphic and univalent in the exterior of the unit circle $ \vert z\vert = 1$. These inequalities disprove two conjectures of Schober about linear functionals on $ \Sigma $.


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

  • [1] P. L. Duren, Univalent functions, Springer-Verlag, New York, 1983. MR 708494 (85j:30034)
  • [2] L. Liu, Some inequalities derived from fundamental lemma concerning Schlicht functions, Acta Math. Sinica 7 (1957), 313-326. (Chinese) MR 0101326 (21:138)
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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1086333-2
Keywords: Univalent functions, coefficient inequalities, support points
Article copyright: © Copyright 1992 American Mathematical Society

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