Inequalities for inner radii of symmetric disjoint domains - Bakhtin, A. K.; Vyhovs'ka, L.V.; Denega, I. V. (Ukrains’kyi Matematychnyi Zhurnal, 2018)
We study the following problem: Let $a_0 = 0, | a_1| = ... = | a_n| = 1,\; a_k \in B_k {\subset C}$, where $B_0, ... ,B_n$ are disjoint domains, and $B_1, ... ,B_n$ are symmetric about the unit circle. It is necessary to find the exact upper bound for$r^{γ} (B_0, 0) \prod^n_{k=1}r(B_k, a_k)$, where $r(B_k, a_k)$ is the inner radius of Bk with respect to $a_k$.For $γ = 1$ and $n ≥ 2$, the problem was solved by L. V. Kovalev. We solve this problem for $γ \in (0, γ_n], γ_n = 0,38 n^2$,and $n ≥ 2$ under the additional assumption imposed on the angles between the neighboring line segments $[0, a_k]$.