Advertisement

Siberian Mathematical Journal

, Volume 26, Issue 1, pp 37–50 | Cite as

Coefficient inequalities for conformal mappings with homeomorphic continuation

  • A. Z. Grinshpan
Article

Keywords

Conformal Mapping Coefficient Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    N. A. Lebedev, The Area Principle in the Theory of Single-Sheeted Functions [in Russian], Nauka, Moscow (1975).Google Scholar
  2. 2.
    A. Z. Grinshpan and Z. D. Kolomoitseva, “The area method for functions with no common values,” Vestn. Leningr. Univ., Ser. Mat., Mekh. Astron., No. 19, 31–36 (1979).Google Scholar
  3. 3.
    I. M. Milin, Single-Sheeted Functions and Orthonormed Systems [in Russian], Nauka, Moscow (1971).Google Scholar
  4. 4.
    O. Lehto, “Schlicht functions with a quasiconformal extension,” Ann. Acad. Sci. Fenn. Suomolais Tiedeakat. Toimituks, Ser. AI,500, 10 (1971).Google Scholar
  5. 5.
    R. Kühnau, “Verzuerrungssätze und Koeffizientenbedingungen von Grunsky'schen Typ für quasikonforme Abbildungen,” Math. Nachr.,48, 77–105 (1971).Google Scholar
  6. 6.
    V. Ya. Gutlyanskii, “On the area principle for a class of quasiconformal mappings,” Dokl. Akad. Nauk SSSR,212, No. 3, 540–543 (1973).Google Scholar
  7. 7.
    V. G. Sheretov, “On a variant of the area theorem,” Matematicheskii Analiz, Krasnodar,217, No. 3, 77–80 (1976).Google Scholar
  8. 8.
    V. A. Shchepetev, “An area theorem for a class of quasiconformal mappings,” in: Extremal Problems in Function Theory [in Russian], Tomsk (1979), pp. 69–85.Google Scholar
  9. 9.
    G. E. Shilov and B. L. Gurevich, Integral, Measure, and Derivative [in Russian], Nauka, Moscow (1967).Google Scholar
  10. 10.
    L. Ahlfors, Lectures on Quasiconformal Mappings [Russian translation], Mir, Moscow (1969).Google Scholar
  11. 11.
    S. L. Sobolev, Applications of Functional Analysis in Mathematical Physics, Amer. Math. Soc. (1969).Google Scholar
  12. 12.
    D. Aharonov, “A generalization of a theorem of J. A. Jenkins,” Math. Z.,110, 218–222 (1969).Google Scholar
  13. 13.
    A. Z. Grinshpan, “An application of the area principle to Biberbach-Eulenberg functions,” Mat. Zametki,11, No. 6, 609–618 (1972).Google Scholar
  14. 14.
    R. Kühnau, “Zu den Grunskyschen Coeffizientenbedingungen,”, Ann. Acad. Sci. Fenn., Ser. A1,6, 125–130 (1981).Google Scholar
  15. 15.
    L. V. Ahlfors, “Remarks on the Neumann-Poincare integral equation,”, Pac. J. Math.,2, 271–280 (1952).Google Scholar
  16. 16.
    S. L. Krushkal', “A remark on the domain of values of analytic functionals on classes of conformal and quasiconformal mappings,” Sib. Mat. Zh.,23, No. 4, 90–98 (1982).Google Scholar
  17. 17.
    A. Z. Grinshpan, “On the growth of the coefficients of single-sheeted functions with quasiconformal continuation,” Sib. Mat. Zh.,23, No. 2, 208–211 (1982).Google Scholar
  18. 18.
    D. Horowitz, “A further refinement for coefficient estimates of univalent functions,” Proc. Am. Math. Soc.,71, No. 2, 217–221 (1978).Google Scholar
  19. 19.
    A. Z. Grinshpan, “An improved estimate for the difference in modulus of the coefficients of single-sheeted functions,” in: Some Problems in Contemporary Function Theory [in Russian], Novosibirsk (1976), pp. 41–45.Google Scholar
  20. 20.
    A. Z. Grinshpan, “On the coefficients of powers of single-sheeted functions,”, Sib. Mat. Zh.,22, No. 4, 88–93 (1981).Google Scholar
  21. 21.
    S. A. Gel'fer, “A class of regular functions which do not take any pair of values w and-w,” Mat. Sb.,19 (61), No. 1, 33–46 (1946).Google Scholar
  22. 22.
    A. E. Grinshpan, “On the coefficients of single-sheeted functions which do not take any pair of values w and-w,” Mat. Zametki,11, No. 1, 3–14 (1972).Google Scholar
  23. 23.
    J. A. Hummel, “A variational method for Gel'fer functions,” J. d'Anal. Math.,30, 271–280 (1976).Google Scholar
  24. 24.
    A. Z. Grinshpan, “On the Taylor coefficients of certain classes of single-sheeted functions,” in Metric Problems in Function Theory [in Russian], Sb. Nauch. Trudov, Naukova Dumka, Kiev (1980), pp. 28–32.Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • A. Z. Grinshpan

There are no affiliations available

Personalised recommendations