Abstract
Some results related to extremal problems with free poles on radial systems are generalized. They are obtained by applying the known methods of geometric function theory of complex variable. Sufficiently good numerical results for γ are obtained.
Highlights
In geometric function theory of complex variable extremal problems on non-overlapping domains form the well-known classic direction
Topics connected with the study of problems on nonoverlapping domains was developed in papers [1]–[21]
This paper summarizes some results obtained in [5], [2]
Summary
In geometric function theory of complex variable extremal problems on non-overlapping domains form the well-known classic direction. Extremal problems on non-overlapping domains, inner radius, n-radial system of points, separating transformation. Let Ω(k1), k = 1, n be a domain of the plane Cζ obtained by combining the connected component πk(Bk P k) containing a point πk(ak), with its symmetrical reflection with respect to the imaginary axis. By Ω(k2), k = 1, n, we denote the domain of the plane Cζ, obtained by combining the connected component πk(Bk+1 P k), containing the point. By Ω(k0) we denote the domain of Cζ, obtained by combining the connected component πk(B0 P k), containing the point ζ = 0, with its symmetrical reflection with respect to the imaginary axis.
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