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On coefficient regions of univalent functions

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Bibliography

  1. V. G. Boltyanski, R. V. Gamkrelidze and L. S. Pontryagin,Theory of optimal processes, Izv. Akad. Nauk SSSR Ser. Mat.24 (1960), 3–42.

    MathSciNet  Google Scholar 

  2. E. Bombieri,On the local maximum property of the Koebe function, Invent. Math.4 (1967), 26–67.

    Article  MATH  MathSciNet  Google Scholar 

  3. S. Friedland,On a conjecture of Robertson, Arch. Rational Mech. Anal.37 (1970), 255–261.

    Article  MATH  MathSciNet  Google Scholar 

  4. P. R. Garabedian and M. Schiffer,A proof of the Bieberbach conjecture for the fourth coefficient, J. Rational Mech. Anal.4 (1955), 427–465.

    MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  6. G. S. Goodman,Univalent Functions and Optimal Control, Ph. D. Thesis, Stanford University, 1968.

  7. G. M. Goluzin,Geometric Theory of Functions of a Complex Variable, Amer. Math. Soc., Providence, R. I., 1969.

    MATH  Google Scholar 

  8. J. L. Kazdan,A boundary value problem arising in the theory of univalent functions, J. Math. Mech.13 (1964), 283–303.

    MATH  MathSciNet  Google Scholar 

  9. K. Loewner,Untersuchungen über schlichte konforme Abbildungen des Einheitskreises I, Math. Ann.89 (1923), 103–121.

    Article  MathSciNet  MATH  Google Scholar 

  10. M. Ozawa,On the Bieberbach conjecture for the sixth coefficient, (Kodai) Math. Sem. Rep.21 (1969), 97–128.

    Article  MATH  MathSciNet  Google Scholar 

  11. R. N. Pederson,A proof of the Bieberbach conjecture for the sixth coefficient, Arch. Rational Mech. Anal.31 (1968), 331–351.

    Article  MATH  MathSciNet  Google Scholar 

  12. R. N. Pederson and M. Schiffer,A proof of the Bieberbach conjecture for the fifth coefficient, Arch. Rational Mech. Anal.45 (1972), 161–193.

    Article  MATH  MathSciNet  Google Scholar 

  13. M. S. Robertson,A remark on the odd schlicht functions, Bull. Amer. Math. Soc.42 (1936), 366–370.

    Article  MATH  MathSciNet  Google Scholar 

  14. A. C. Schaeffer and D. C. Spencer,Coefficient Regions for Schlicht Functions, Amer. Math. Soc. Colloquium Series, vol. 35, Providence, R. I., 1950.

  15. A. C. Schaeffer, M. Schiffer and D. C. Spencer,The coefficient regions of schlicht functions, Duke Math. J.16 (1949), 493–527.

    Article  MATH  MathSciNet  Google Scholar 

  16. M. Schiffer,A method of variation within the family of simple functions, Proc. London Math. Soc.44 (1938), 432–449.

    Article  MATH  Google Scholar 

  17. M. Schiffer,Sur l'équation différentielle de M. Loewner, C. R. Acad. Sci. Paris221 (1945). 369–371.

    MathSciNet  Google Scholar 

  18. M. Schiffer,On the coefficient problem for univalent functions, Trans. Amer. Math. Soc.134 (1968), 95–101.

    Article  MATH  MathSciNet  Google Scholar 

  19. O. Teichmüller,Ungleichungen zwischen den Koeffizienten schlichter Funktionen, Preuss. Akad. Wiss. Sitzungsber. (1938), 363–375.

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This work was supported in part by NSF grant MPS 72-04967A02.

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Friedland, S., Schiffer, M. On coefficient regions of univalent functions. J. Anal. Math. 31, 125–168 (1977). https://doi.org/10.1007/BF02813301

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