Extension of Szego¨'s theorem on the sections of univalent functions
Extension of Szego¨'s theorem on the sections of univalent functions
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DOI：
10.1137/0519107
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发表时间：
1988-10
影响因子：
2
通讯作者：
S. Ruscheweyh
中科院分区：
文献类型：
--
作者：
S. Ruscheweyh
In this paper a far-reaching extension of Szego’s theorem on the univalence of partial sums of the power series expansion of univalent functions in the class $\mathcal{S}$ is given. In particular, it is shown that the property “univalent” can be replaced by the stronger one “starlike univalent” and that the conclusion is not only true for $\mathcal{S}$ but also for the closed convex hull of $\mathcal{S}$. The paper concludes with the discussion of a new conjecture on $\mathcal{S}$, stronger than the former “Bieberbach conjecture.”
