Estimation of the product of inner radii of partially nonoverlapping domains

Abstract

We present new results on the maximization of products of positive powers of inner radii of some special domain systems in the extended complex plane $\overline{{\mathbb C}}$ with respect to points of finite sets such that any two distinct points $z_1, z_2 \in {\mathbb C}\setminus \{0\}$ of such set belong to different rays emerging from the origin.