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Proceedings of the American Mathematical Society

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The radius of close-to-convexity of functions of bounded boundary rotation


Authors: H. B. Coonce and M. R. Ziegler
Journal: Proc. Amer. Math. Soc. 35 (1972), 207-210
MSC: Primary 30A32
DOI: https://doi.org/10.1090/S0002-9939-1972-0296274-3
MathSciNet review: 0296274
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Abstract: An analytic function whose boundary rotation is bounded by $ k\pi (k \geqq 2)$ is shown to map a disc of radius $ {r_k}$ onto a close-to-convex domain, where $ {r_k}$ is the solution of a transcendental equation when $ k > 4$ and $ {r_k} = 1$ when $ 2 \leqq k \leqq 4$. The above value of $ {r_k}$ is shown to be the best possible for each k and an asymptotic expression for $ {r_k}$ is obtained.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0296274-3
Keywords: Bounded boundary rotation, radius of close-to-convexity
Article copyright: © Copyright 1972 American Mathematical Society

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