TY - JOUR
AU - A. K. Bakhtin
AU - L.V. Vyhovs'ka
AU - I. V. Denega
PY - 2018/09/25
Y2 - 2022/10/06
TI - Inequalities for inner radii of symmetric disjoint
domains
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 70
IS - 9
SE - Short communications
DO -
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/1634
AB - 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$r^{\gamma} (B_0, 0) \prod^n_{k=1}r(B_k, a_k)$, where $r(B_k, a_k)$ is the inner radius of Bk with respect to $a_k$.For $\gamma = 1$ and $n \geq 2$, the problem was solved by L. V. Kovalev. We solve this problem for $\gamma \in (0, \gamma_n], \gamma_n = 0,38 n^2$,and $n \geq 2$ under the additional assumption imposed on the angles between the neighboring line segments $[0, a_k]$.
ER -