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Robertson's conjecture on the coefficients of close-to-convex functions


Author: Y. Leung
Journal: Proc. Amer. Math. Soc. 76 (1979), 89-94
MSC: Primary 30C45
DOI: https://doi.org/10.1090/S0002-9939-1979-0534395-4
MathSciNet review: 534395
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Abstract: We use an inequality due to Lebedev and Milin to prove a conjecture made by M.S. Robertson on the coefficients of close-to-convex functions.


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

  • [1] D. Aharonov, Special topics in univalent functions, Lecture notes, Univ. Maryland, 1971.
  • [2] T. H. MacGregor, An inequality concerning analytic functions with a positive real part, Canad. J. Math. 21 (1969), 1172-1177. MR 0249635 (40:2878)
  • [3] Christian Pommerenke, Univalent functions, Vandenhoeck & Ruprecht, Göttingen, 1975. MR 0507768 (58:22526)
  • [4] M. O. Reade, On close-to-convex univalent function, Michigan Math. J. 3 (1955), 59-62. MR 0070715 (17:25c)
  • [5] M. S. Robertson, Quasi-subordination and coefficient conjectures, Bull. Amer. Math. Soc. 76 (1970), 1-9. MR 0251210 (40:4441)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0534395-4
Keywords: Close-to-convex univalent functions, Lebedev-Milin inequality
Article copyright: © Copyright 1979 American Mathematical Society

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