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On meromorphic univalent functions omitting a disc

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Abstract

The class Σb is defined to consist of meromorphic univalent functionsH omitting a disc with the radiusb:H(z)=z+ Σ ∞0 A n z −n,z>1,H(b)>b ∈ (0, 1). By aid of FitzGerald inequalities the inverse coefficients of odd Σb-functions are maximized. The result extends the corresponding estimation, due to Netanyahu and Schober, fromb=0 to the whole interval (0, 1).

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References

  1. C. FitzGerald,Quadratic inequalities and coefficient estimates for schlicht functions, Arch. Rat. Mech. Anal.46 (1972), 356–368.

    Article  MATH  MathSciNet  Google Scholar 

  2. G. M. Goluzin,Geometric Theory of Functions of a Complex Variable, Vol. 26, Amer. Math. Soc., Providence, R.I., 1969.

    Google Scholar 

  3. E. Launonen,On exponentiated Grunsky inequalities for bounded univalent functions, Ann. Acad. Sci. Fenn., Ser. A I Math., Dissertationes1 (1975), 1–34.

    Google Scholar 

  4. E. Netanyahu,Extremal problems for schlicht functions in the exterior of the unit circle, Can. J. Math.17 (1965), 335–341.

    MATH  MathSciNet  Google Scholar 

  5. G. Schober,Coefficients of inverses of meromorphic univalent functions, Proc. Amer. Math. Soc.67 (1977), 111–116.

    Article  MATH  MathSciNet  Google Scholar 

  6. V. Singh,Grunsky inequalities and coefficients of bounded schlicht functions, Ann. Acad. Sci. Fenn., Ser. A I Math.310 (1962), 1–21.

    Google Scholar 

  7. O. Tammi,Grunsky type of inequalities, and determination of the totality of the extremal functions, Ann. Acad. Sci. Fenn. Ser. A I443 (1969), 1–10.

    MathSciNet  Google Scholar 

  8. O. Tammi,Extremum problems for bounded univalent functions, Lecture Notes in Mathematics646, Springer-Verlag, Berlin-Heidelberg-New York, 1978, pp. 1–313.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Lódź, ul. Narutowicza Nr 65, Poland

    Henryka Siejka

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  1. Henryka Siejka
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Additional information

The author wishes to express her gratitude to Professor O. Tammi for valuable discussions connected with the problem.

This work was supported by a grant from the Finnish Ministry of Education.

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Siejka, H. On meromorphic univalent functions omitting a disc. Israel J. Math. 54, 291–300 (1986). https://doi.org/10.1007/BF02764957

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  • DOI: https://doi.org/10.1007/BF02764957

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