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Lagrange multipliers in variational methods for univalent functions

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References

  1. L. V. Ahlfors,Conformal Invariants, McGraw-Hill, New York, 1973.

    MATH  Google Scholar 

  2. G. M. Golusin,Geometric theory of functions of a complex variable, Trans. Math. Monographs, Vol. 26, Amer. Math. Soc., Providence, R.I., 1969.

    Google Scholar 

  3. J. A. Hummel,A variational method for starlike functions, Proc. Amer. Math. Soc.9 (1958), 82–87.

    Article  MATH  MathSciNet  Google Scholar 

  4. J. A. Hummel and M. M. Schiffer,Variational methods for Bieberbach-Eilenberg functions and for Pairs, to appear in Ann. Acad. Sci. Fenn.

  5. F. Marty,Sur le module des coefficients de MacLaurin d'une fonction univalent, C. R. Acad. Sci. Paris198 (1934), 1569–1571.

    Google Scholar 

  6. E. Netanyahu,On univalent functions in the unit disc whose image contains a given disc, J. Analyse Math.23 (1970), 305–322.

    MATH  MathSciNet  Google Scholar 

  7. G. Piranian,An isolated schlicht function, Abh. Math. Sem. Univ. Hamburg24 (1960), 236–238.

    Article  MATH  MathSciNet  Google Scholar 

  8. Chr. Pommerenke,Univalent Functions, Vandenhoeck and Ruprecht, Göttingen, 1975.

    MATH  Google Scholar 

  9. 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 

  10. A. C. Schaeffer and D. C. Spencer,Coefficient regions for schlicht functions, Amer. Math. Soc. Colloquium Publ., Vol. 35, Amer. Math. Soc., New York, 1950.

    MATH  Google Scholar 

  11. A. C. Schaeffer, M. Schiffer, and D. C. Spencer,The coefficient regions of schlicht functions, Duke Math. J.16 (1949), 493–526.

    Article  MATH  MathSciNet  Google Scholar 

  12. M. Schiffer,A method of variations within the family of simple functions, Proc. London Math. Soc. (2)44 (1938), 432–449.

    Article  MATH  Google Scholar 

  13. M. Schiffer,Extremal problems and variational methods in conformal mapping, Proc. International Congress Math., Edinburgh (1958), 213–231.

  14. G. Schober,Univalent Functions—Selected Topics, Lecture Notes in Math. 478, Springer-Verlag, Berlin, 1975.

    MATH  Google Scholar 

  15. V. Singh,Interior variations and some extremal problems for certain classes of univalent functions, Pacific J. Math.7 (1957), 1485–1504.

    MATH  MathSciNet  Google Scholar 

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This research was supported in part by the Samuel Neaman Fund, Special Year in Complex Analysis, Technion—ITT, Haifa, Israel and in part by the National Science Foundation grant number MCS 75-07387A01 to the University of Maryland, College Park, Maryland.

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Hummel, J.A. Lagrange multipliers in variational methods for univalent functions. J. Anal. Math. 32, 222–234 (1977). https://doi.org/10.1007/BF02803581

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