Abstract:
The paper deals with the following problem, stated in [Zbl.830.30014] by V. N. Dubinin and earlier, in different form, by G. P. Bakhtina [Zbl.585.30027]. Let $a_0=0$, $|a_1|=\dots=|a_n|=1$, $a_k\in B_k\in\overline{\mathbb C}$, where $B_0,\dots,B_n$ are disjoint domains, and $B_1,\dots,B_n$ are symmetric about the unit circle. Find the exact upper bound for $\prod_{k=0}^n r(B_k,a_k)$, where $r(B_k,a_k)$ is the inner radius radius of $B_k$ with respect to $a_k$. For $n\ge3$ this problem was recently solved by the author. In the present paper, it is solved for $n=2$.
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