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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
Correction: Proc. Amer. Math. Soc. 120 (1994), null.
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] 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)
  • [3] G. Schober, Univalent functions--selected topics, Lecture Notes in Math., vol. 478, Springer-Verlag, Berlin, Heidelberg, and New York, 1975. MR 0507770 (58:22527)
  • [4] -, Some conjectures for the class $ \Sigma $, in Topics in complex analysis, Contemp. Math., vol. 38, Amer. Math. Soc., Providence, R.I., 1985, pp. 13-21. MR 789441

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Keywords: Univalent functions, coefficient inequalities, support points
Article copyright: © Copyright 1992 American Mathematical Society

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