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Proceedings of the American Mathematical Society

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Radius of starlikeness of convex combinations of univalent starlike functions


Authors: D. H. Hamilton and P. D. Tuan
Journal: Proc. Amer. Math. Soc. 78 (1980), 56-58
MSC: Primary 30C45
MathSciNet review: 548084
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Abstract: The radius of starlikeness of the convex combination

$\displaystyle tf(z) + (1 - t)g(z),\quad 0 < t < 1,$

where $ f(z)$ and $ g(z)$ are normalized univalent starlike functions, is $ {r_u} = 0.4035 \ldots $, the positive root of the equation $ {r^6} + 5{r^4} + 79{r^2} - 13 = 0$.

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DOI: https://doi.org/10.1090/S0002-9939-1980-0548084-1
Keywords: Radius of starlikeness, closed convex hull of starlike univalent functions, Hadamard product
Article copyright: © Copyright 1980 American Mathematical Society