On coefficient inequalities for meromorphic univalent functions
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- by Li Quan Liu PDF
- Proc. Amer. Math. Soc. 114 (1992), 413-422 Request permission
Correction: Proc. Amer. Math. Soc. 120 (1994), 1319.
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 $|z| = 1$. These inequalities disprove two conjectures of Schober about linear functionals on $\Sigma$.References
- Peter L. Duren, Univalent functions, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 259, Springer-Verlag, New York, 1983. MR 708494
- Li-Chuan Liu, Some inequalities derived from fundamental lemma concerning schlicht functions, Acta Math. Sinica 7 (1957), 313–326 (Chinese, with English summary). MR 101326
- Glenn Schober, Univalent functions—selected topics, Lecture Notes in Mathematics, Vol. 478, Springer-Verlag, Berlin-New York, 1975. MR 0507770
- Glenn Schober, Some conjectures for the class $\Sigma$, Topics in complex analysis (Fairfield, Conn., 1983) Contemp. Math., vol. 38, Amer. Math. Soc., Providence, RI, 1985, pp. 13–21. MR 789441, DOI 10.1090/conm/038/02
Additional Information
- © Copyright 1992 American Mathematical Society
- 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
- MathSciNet review: 1086333