Skip to main content
SpringerLink
Log in

Keldysh-Sedov formulas and differentiability with respect to the parameter of families of univalent functions inn-connected domains

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

We introduce families of functionsF j(w, t) mapping (n+1)-connected domains onto circular domains in thez-plane. Denote by Φ j (z, t) the families of functions inverse toF j(w, t). Theorems 1–4 treat differentiability properties of these families with respect tot at a pointt=t 0. We present formulas for the first derivative with respect tot. Corollaries of the theorems obtained are given. As a particular case, we deduce the theorem due to Kufarev for the disk and the theorem of Kufarev and Genina (Semukhina) for the annulus.

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. A. S. Sorokin, “The variational method of Goluzin-Kufarev and formulas of Keldysh-Sedov,”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],308, No. 2, 273–277 (1989).

    Google Scholar 

  2. A. S. Sorokin, “A problem of Keldysh-Sedov for multiconnected circular domains,”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],293, No. 1, 41–44 (1987).

    MATH  MathSciNet  Google Scholar 

  3. A. S. Sorokin, “A problem of Keldysh-Sedov for multiconnected circular domains,”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],296, No. 4, 801–804 (1987).

    MathSciNet  Google Scholar 

  4. P. P. Kufarev, “On one-parameter families of analytic functions,”Mat. Sb. [Math. USSR-Sb.],13, No. 55, 87–117 (1943).

    Google Scholar 

  5. P. P. Kufarev, “On a property of extremal domains for a problem of coefficients,”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],97, No. 4, 391–393 (1954).

    MATH  MathSciNet  Google Scholar 

  6. P. P. Kufarev and N. V. Genina (Semukhina), “On an extension of a variational method due to Goluzin to two-connected domains,”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],107, No. 4, 505–507 (1956).

    MathSciNet  Google Scholar 

  7. N. V. Genina, “On an extension of a variational method due to Goluzin to two-connected domains,”Uchen. Zap. Tomsk Univ., No. 144, 226–240 (1962).

    Google Scholar 

  8. G. M. Goluzin,Geometrical Theory of Functions of Complex Variable [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  9. I. A. Aleksandrov and A. S. Sorokin, “On an extension of a variational method due to Goluzin-Kufarev to multiconnected domains,”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],161, No. 6, 1207–1210 (1967).

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Siberean Metallurgical Institute, Novokuznetsk

    A. S. Sorokin

Authors
  1. A. S. Sorokin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromMatematicheskie Zametki, Vol. 58, No. 6, pp. 878–889, December, 1995.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sorokin, A.S. Keldysh-Sedov formulas and differentiability with respect to the parameter of families of univalent functions inn-connected domains. Math Notes 58, 1306–1314 (1995). https://doi.org/10.1007/BF02304890

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02304890

Keywords

Search

Navigation