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The paper deals with the following open problem stated by V.N. Dubinin. Let $a_{0}=0$, $|a_{1}|=\ldots=|a_{n}|=1$, $a_{k}\in B_{k}\subset \overline{\mathbb{C}}$, where $B_{0},\ldots, B_{n}$ are disjoint domains. For all values of the parameter $\gamma\in (0, n]$ find the exact upper bound for $r^\gamma(B_0,0)\prod\limits_{k=1}^n r(B_k,a_k)$, where $r(B_k,a_k)$ is the conformal radius of $B_k$ with respect to $a_k$. For $\gamma=1$ and $n\geqslant2$ the problem was solved by V.N. Dubinin. In the paper the problem is solved for $\gamma\in (0, \sqrt{n}\,]$ and $n\geqslant2$ for simply connected domains.The paper deals with the following open problem stated by V.N. Dubinin. Let a 0  = 0, ι a  1 ι =...= ιa  n  ι = 1, a  k  ∈ B k   ⊂ , where  B  0,   ..., B  n  are disjoint domains. For all values of the parameter γ∈ (0;  n ] find the exact upper bound   n  for  r  γ ( B 0  ; 0) ∏  r (B  k  ; a  k  ), where  r (B  k  ; a  k  ) is the conformal radius of B  k   with respect to a  k  . For  γ  = 1  k=1  and  n  ≥ 2 the problem was solved by V.N. Dubinin. In the paper the problem is solved for γ ∈ (0; √ n  ] and  n ≥  2 for simply connected domains.

On Conformal Radii of Non-Overlapping Simply Connected Domains