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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The Zalcman conjecture for close-to-convex functions


Author: Wan Cang Ma
Journal: Proc. Amer. Math. Soc. 104 (1988), 741-744
MSC: Primary 30C50; Secondary 30C45
DOI: https://doi.org/10.1090/S0002-9939-1988-0964850-X
MathSciNet review: 964850
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Abstract: Let $ S$ be the class of functions $ f(z) = z + \cdots $ analytic and univalent in the unit disk $ D$. For $ f(z) = z + {a_2}{z^2} + \cdots \in S$, Zalcman conjectured that $ \vert a_n^2 - {a_{2n - 1}}\vert\; \leq \;{(n - 1)^2}(n = 2,3, \ldots )$. This conjecture is verified for $ n \geq 4$ and close-to-convex functions.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0964850-X
Article copyright: © Copyright 1988 American Mathematical Society