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A coefficient problem for bounded nonvanishing functions

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References

  1. R. P. Boas,Entire Functions, Academic Press, New York, 1954.

    MATH  Google Scholar 

  2. Louis Brickman,Extremal problems for certain classes of analytic functions, Proc. Amer. Math. Soc.35 (1972), 67–73.

    Article  MATH  MathSciNet  Google Scholar 

  3. J. Clunie and Ch. Pommerenke,On the coefficients of univalent functions, Michigan Math. J.14 (1967), 71–78.

    Article  MATH  MathSciNet  Google Scholar 

  4. H. B. Coonce,A variational method for functions of bounded boundary rotation, Trans. Amer. Math. Soc.157 (1971), 39–51.

    Article  MATH  MathSciNet  Google Scholar 

  5. P. L. Duren,Theory of H p Spaces, Academic Press, New York, 1970.

    MATH  Google Scholar 

  6. P. L. Duren and M. Schiffer,A variational method for functions schlicht in an annulus, Arch. Rat. Mech. Anal.9 (1962), 260–272.

    Article  MATH  MathSciNet  Google Scholar 

  7. J. M. Galperin,Some estimates for functions bounded in the unit disc, Uspehi Mat. Nauk20 (121) (1965), 197–202.

    MathSciNet  Google Scholar 

  8. G. M. Golusin,Geometric Theory of Functions of a Complex Variable, American Mathematical Society, Providence, 1969.

    Google Scholar 

  9. W. K. Hayman,Multivalent Functions, Cambridge University Press, 1958.

  10. J. A. Hummel,The coefficient regions of starlike functions, Pacific J. Math.7 (1957), 1381–1389.

    MATH  MathSciNet  Google Scholar 

  11. W. E. Kirwan,Extremal problems for the typically real functions, Amer. J. Math.88 (1966), 942–954.

    Article  MATH  MathSciNet  Google Scholar 

  12. J. Krzyż,Coefficient problem for bounded nonvanishing functions, Ann. Polon. Math.20 (1968), 314.

    Google Scholar 

  13. V. Levin,Aufgabe 163, Jber. Deutsch. Math.-Verein.43 (1933), 113; Lösung,ibid. Jber. Deutsch. Math.-Verein.44 (1934). 80–83 (solutions by W. Fenchel and E. Reissner).

    Google Scholar 

  14. Zeev Nehari,A proof of |a 4 |≦4 by Loewner's method, inSymposium on Complex Analysis Canterbury, 1974. J. Clunie and W. K. Hayman (eds.), Cambridge University Press, 1974.

  15. C. T. Rajagopal,On inequalities for analytic functions, Amer. Math. Monthly60 (1953), 693–695.

    Article  MATH  MathSciNet  Google Scholar 

  16. M. S. Robertson,A variational method for functions with positive real part, Trans. Amer. Math. Soc.102 (1962), 82–93.

    Article  MATH  MathSciNet  Google Scholar 

  17. Werner Rogosinski,On the coefficients of subordinate functions, Proc. London Math. Soc. (2)48 (1945), 48–82.

    Article  MathSciNet  Google Scholar 

  18. K. Sakaguchi,A variational method for functions with positive rela part, J. Math. Soc. Japan16 (1964), 287–296.

    Article  MATH  MathSciNet  Google Scholar 

  19. H. S. Shapiro,Problem 4468, Amer. Math. Monthly59 (1952), 45;solution (by M. S. Robertson)ibid. Amer. Math. Monthly60 (1953), 131–132.

    Article  MathSciNet  Google Scholar 

  20. Gabor Szegö,Orthogonal Polynomials, American Mathematical Society, New York, 1939.

    Google Scholar 

  21. M. Tsuji,Potential Theory in Modern Function Theory, Maruzen, Tokyo, 1959.

    MATH  Google Scholar 

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Hummel, J.A., Scheinberg, S. & Zalcman, L. A coefficient problem for bounded nonvanishing functions. J. Anal. Math. 31, 169–190 (1977). https://doi.org/10.1007/BF02813302

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