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Starlikeness, convexity and other geometric properties of holomorphic maps in higher dimensions

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References

  1. J. W. Alexander, Functions which map the interior of the unit circle upon simple regions, Annals of Math. 17 (1915), 12–22.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. M. Biernacki, Sur la représentation conforme des domaines linéairement accessible, Prace Frat. Fiz. 44 (1937), 293–314.

    MATH  Google Scholar 

  3. S. Bochner and W. T. Martin, Several Complex Variables, Princeton University Press, 1948.

    Google Scholar 

  4. K. R. Gurganus, Φ-like holomorphic functions in C n and Banach spaces, Trans. Amer. Math. Soc. 205 (1975), 389–406.

    MathSciNet  MATH  Google Scholar 

  5. L. A. Harris, Schwarz's Lemma in normed linear spaces, Proc. Natl. Acad. Sci. U.S.A. 64(4), (1969), 1014–1017.

    CrossRef  MATH  Google Scholar 

  6. E. Hille and R. S. Phillips, Functional Analysis and Semigroups, Amer. Math. Soc. Colloq. Publ. 31 (1957).

    Google Scholar 

  7. W. Kaplan, Close-to-convex schlicht functions, Michigan Math. J. 1 (1952), 169–185.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Z. Lewandowski, Sur l'identité de certaines classes de fonctions univalentes, I and II, Ann. Univ. Mariae Curie-Sklodowska, Sect. A, 12 (1958), 131–146 and 14 (1960), 19–46.

    MathSciNet  Google Scholar 

  9. T. Matsuno, Starlike theorems and convex-like theorems in the complex vector space, Sci. Rep. Toko, Kyoiku Daigaku, Sect. A, 5 (1955), 88–95.

    MathSciNet  MATH  Google Scholar 

  10. J. A. Pfaltzgraff, Subordination chains and univalence of holomorphic mappings on C n, Math. Ann. 210 (1974), 55–68.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. J. A. Pfaltzgraff and T. J. Suffridge, Close-to-starlike holomorphic functions of several variables, Pac. J. Math. 57 (1975), 271–279.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. Ch. Pommerenke, Über die Subordination analytischer Funktionen, J. Reine Angew. Math. 218 (1965), 159–173.

    MathSciNet  MATH  Google Scholar 

  13. M. S. Robertson, Applications of the subordination principle to univalent functions, Pac. J. Math. 11 (1961), 315–324.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. L. Spaček, Contibution à la theorie des fonctions univalentes, Časopsis Pěct. Mat. 62 (1932), 12–19.

    MATH  Google Scholar 

  15. T. J. Suffridge, The principle of subordination applied to functions of several variables, Pac. J. Math. 33 (1970), 241–248.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. —, Starlike and convex maps in Banach spaces, Pac. J. Math. 46 (1973), 575–589.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1977 Springer-Verlag

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Suffridge, T.J. (1977). Starlikeness, convexity and other geometric properties of holomorphic maps in higher dimensions. In: Buckholtz, J.D., Suffridge, T.J. (eds) Complex Analysis. Lecture Notes in Mathematics, vol 599. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096834

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  • DOI: https://doi.org/10.1007/BFb0096834

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  • Publisher Name: Springer, Berlin, Heidelberg

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