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Siberian Mathematical Journal

, Volume 43, Issue 2, pp 379–387 | Cite as

On the Coefficient Problem for Univalent Functions

  • V. G. Sheretov
Article
  • 34 Downloads

Abstract

We prove a criterion for analytic functions to belong to the classes S(p) and Σ(p) of univalent functions with p-multiple circular symmetry in terms of countable systems of exact coefficient inequalities. As a consequence we obtain a description for the corresponding domains of coefficients.

Keywords

Analytic Function Univalent Function Countable System Circular Symmetry Coefficient Problem 
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References

  1. 1.
    De Branges L., “A proof of the Bieberbach conjecture,” Acta Math., 154, 137-152 (1985).Google Scholar
  2. 2.
    Aleksandrov I. A., Parametric Extensions in the Theory of Univalent Functions [in Russian], Nauka, Moscow (1976).Google Scholar
  3. 3.
    Lebedev N. A., The Area Principle in the Theory of Univalent Functions [in Russian], Nauka, Moscow (1975).Google Scholar
  4. 4.
    Milin I. M., Univalent Functions and Orthonormal Systems [in Russian], Nauka, Moscow (1971).Google Scholar
  5. 5.
    Sheretov V. G., Analytic Functions with Quasiconformal Continuation, Tversk. Gos. Univ., Tver' (1991).Google Scholar
  6. 6.
    Schaeffer A. C. and Spencer D. C., Coefficient Regions for Schlicht Functions, Amer. Math. Soc., New York (1950).Google Scholar
  7. 7.
    Sheretov V. G., Quasiconformal Mappings That Are Extremal for Their Boundary Values [in Russian], Dis. Dokt. Fiz.-Mat. Nauk, Kubansk. Univ., Krasnodar (1988).Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • V. G. Sheretov
    • 1
  1. 1.Tver' State UniversityTver'

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