Skip to main content
SpringerLink
Log in

On the bieberbach and Koebe constants for sector domains and sector disks

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

We discuss domain constants related to the classical Bieberbach and Koebe theorems. We find a class of simply connected domains for which the product of these constants behave like extremal domain and gives a better result on Osgood’s inequalities.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. B. Conway,Functions of One Complex Variable II, Springer-Verlag, New York, 1995.

    MATH  Google Scholar 

  2. R. Harmelin and D. Minda,Quasi-invariant domain constants, Israel Journal of Mathematics77 (1992), 115–127.

    Article  MATH  MathSciNet  Google Scholar 

  3. D. Minda,The Schwarzian derivative and univalence criteria, Contemporary Mathematics38 (1985), 43–52.

    MathSciNet  Google Scholar 

  4. B. G. Osgood,Some properties of f″/f′ and the Poincaré metric, Indiana University Mathematics Journal31 (1982), 449–461.

    Article  MATH  MathSciNet  Google Scholar 

  5. Ch. Pommerenke,Linear-invariante Familien Analytischer Funktionen I, Mathematische Annalen155 (1964), 108–154.

    Article  MATH  MathSciNet  Google Scholar 

  6. Ch. Pommerenke,Uniformly perfect sets and the Poincaré metric, Archive der Mathematik32 (1979), 192–199.

    Article  MATH  MathSciNet  Google Scholar 

  7. S. E. Rugeihyamu,On the Koebe and Bieberbach constants for a hyperbolic planar domain, Israel Journal of Mathematics112 (2000), 369–378.

    MathSciNet  Google Scholar 

  8. S. E. Rugeihyamu,On the Koebe and Bieberbach constants for hyperbolic domains, Thesis, National University of Ireland, Cork, Ireland, 1999.

    Google Scholar 

  9. T. Carroll and S. E. Rugeihyamu,On the Bieberbach and Koebe constants of a simply connected domain, Journal of Complex Variables46 (2001), 31–46.

    Article  MATH  MathSciNet  Google Scholar 

  10. S. Yamashita,Univalent analytic functions and the Poincaré metric, Kodai Mathematics Journal13 (1990), 45–48.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Dar-es-Salaam, P.O. Box 35062, Dar-es-Salaam, Tanzania

    Sylvester E. Rugeihyamu

Authors
  1. Sylvester E. Rugeihyamu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sylvester E. Rugeihyamu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rugeihyamu, S.E. On the bieberbach and Koebe constants for sector domains and sector disks. Isr. J. Math. 136, 117–123 (2003). https://doi.org/10.1007/BF02807193

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02807193

Keywords

Search

Navigation