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Proceedings of the American Mathematical Society

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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
MathSciNet review: 1086333
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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] Peter L. Duren, Univalent functions, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 259, Springer-Verlag, New York, 1983. MR 708494
  • [2] Li-Chuan Liu, Some inequalities derived from fundamental lemma concerning schlicht functions, Acta Math. Sinica 7 (1957), 313–326 (Chinese, with English summary). MR 0101326
  • [3] Glenn Schober, Univalent functions—selected topics, Lecture Notes in Mathematics, Vol. 478, Springer-Verlag, Berlin-New York, 1975. MR 0507770
  • [4] Glenn Schober, Some conjectures for the class Σ, Topics in complex analysis (Fairfield, Conn., 1983) Contemp. Math., vol. 38, Amer. Math. Soc., Providence, RI, 1985, pp. 13–21. MR 789441, 10.1090/conm/038/02

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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