Extremal Quasiconformal Mappings with Free Boundary Components in Domains of Arbitray Connectivity.
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.
Let D = z: Re z < 0 and let S*(D) be the class of univalent functions normalized by the conditions , a a finite complex number, 0 ∉ f(D), and mapping D onto a domain f(D) starlike with respect to the exterior point w = 0. Some estimates for |f(z)| in the class S*(D) are derived. An integral formula for f is also given.