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Early coefficients of the inverse of a regular convex function

Authors: Richard J. Libera and Eligiusz J. Złotkiewicz
Journal: Proc. Amer. Math. Soc. 85 (1982), 225-230
MSC: Primary 30C50
MathSciNet review: 652447
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Abstract: Using known properties of functions of positive real part it is shown that the first seven coefficients of the inverse of a regular univalent function mapping the disk onto a convex region are bounded by 1.

References [Enhancements On Off] (What's this?)

  • [1] P. L. Duren, Coefficients of univalent functions, Bull. Amer. Math. Soc. 83 (1977), 891-911. MR 0470182 (57:9943)
  • [2] U. Grenander and G. Szegö, Toeplitz forms and their applications, Univ. of California Press, Berkeley and Los Angeles, 1958. MR 0094840 (20:1349)
  • [3] W. E. Kirwan and G. Schober, Inverse coefficients for functions of bounded boundary rotation, Tech. Rep. TR 79-42, MD 79-49-WK/GS, Univ. of Maryland, 1979. MR 581809 (81j:30026)
  • [4] J. G. Krzyż, R. J. Libera and E. J. Zlotkiewicz, Coefficients of inverses of regular starlike functions, Ann. Univ. Mariae Curie-Skł odowska Sect. A 33 (1979), 103-110. MR 689590 (84d:30027)
  • [5] A. E. Livingston, The coefficients of multivalent close-to-convex functions, Proc. Amer. Math. Soc. 21 (1969), 545-552. MR 0243054 (39:4378)
  • [6] Ch. Pommerenke, Univalent functions, Vandenhoeck and Ruprecht, Göttingen, 1975. MR 0507768 (58:22526)
  • [7] D. V. Prokhorov and J. Szynal, Inverse coefficients for $ (\alpha ,\beta )$-convex functions (preprint).
  • [8] G. Schober, Coefficient estimates for inverses of schlicht functions (preprint). MR 623495 (82j:30021)
  • [9] S. Smale, The fundamental theorem of algebra and complexity theory, Bull. Amer. Math. Soc. 4 (1981), 1-36. MR 590817 (83i:65044)

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