Estimation of the product of inner radii of partially nonoverlapping domains

We present new results on the maximization of products of positive powers of inner radii for several special systems of domains in the extended complex plane {ie1176-01} with respect to points of finite sets such that any two different points z ₁, z ₂ ∈ ℂ \ {0} of such a set lie on different rays that emerge from the origin of coordinates. Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 7, pp. 1004–1008, July, 2008.