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Coefficient inequalities for Bieberbach-Eilenberg functions

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Bibliography

  1. Bieberbach, L., Über die Koeffizienten derjenigen Potenzreihen, welche eine schlichte Abbildung des Einheitskreises vermitteln. Preuss. Akad. Wiss. Berlin, Sitzungsberichte 1916, pp. 940–955.

    Google Scholar 

  2. Bieberbach, L., Über einige Extremalprobleme im Gebiet der konformen Abbildung. Math. Ann. 77, 153–172 (1916).

    Google Scholar 

  3. Charzynski, Z., & M. Schiffer, A new proof of the Bieberbach conjecture for the fourth coefficient. Arch. Rational Mech. Anal. 5, 187–193 (1960).

    Google Scholar 

  4. Eilenberg, S., Sur quelques propriétés topologiques de la surface de sphère. Fund. Math. 25, 267–272(1935).

    Google Scholar 

  5. Garabedian, P.R., G.G. Ross, & M. Schiffer, On the Bieberbach conjecture for even n. J. Math. Mech. 14, 975–989 (1963).

    Google Scholar 

  6. Garabedian, P. R., & M. Schiffer, The local maximum theorem for the coefficients of univalent functions. Arch. Rational Mech. Anal. 26, 1–32 (1967).

    Google Scholar 

  7. Grunsky, H., Koeffizientenbedingungen für schlicht abbildende meromorphe Funktionen. Math. Z. 45, 29–61 (1939).

    Google Scholar 

  8. Jenkins, J.A., Some area theorems and a special coefficient theorem. Illinois J. Math. 8, 80–99 (1964).

    Google Scholar 

  9. Nehari, Z., Some inequalities in the theory of functions. Trans. Amer. Math. Soc. 75, 256–286 (1953).

    Google Scholar 

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Authors and Affiliations

  1. University of Maryland, College Park, Maryland

    James A. Hummel & Menahem Schiffer

  2. Stanford University, Stanford, California

    James A. Hummel & Menahem Schiffer

Authors
  1. James A. Hummel
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  2. Menahem Schiffer
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Additional information

This work was supported in part by the National Science Foundation grant NSF GP 6891 at the University of Maryland and by the Air Force contract AF 49 (638) 1345 at Stanford University.

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Hummel, J.A., Schiffer, M. Coefficient inequalities for Bieberbach-Eilenberg functions. Arch. Rational Mech. Anal. 32, 87–99 (1969). https://doi.org/10.1007/BF00247675

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  • DOI: https://doi.org/10.1007/BF00247675

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