Application of upper estimates for products of inner radii to distortion theorems for univalent functions

Q3 Mathematics Matematychni Studii Pub Date : 2023-12-18 DOI:10.30970/ms.60.2.138-144

I. Denega, Yaroslav V. Zabolotnyi

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Abstract

In 1934 Lavrentiev solved the problem of maximum ofproduct of conformal radii of two non-overlapping simply connected domains. In the case of three or more points, many authors considered estimates of a more general Mobius invariant of the form$$T_{n}:={\prod\limits_{k=1}^nr(B_{k},a_{k})}{\bigg(\prod\limits_{1\leqslant k

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内半径积的上估计值在单值函数变形定理中的应用

1934 年，拉夫连季耶夫解决了两个不重叠的简单相连域的共形半径的最大积问题。在三个或更多点的情况下，许多学者考虑了形式为$$T_{n}的更一般莫比乌斯不变量的估计值：={\prod\limits_{k=1}^nr(B_{k},a_{k})}{\bigg(\prod\limits_{1\leqslant k

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