Vyhivska L. Extremal problems for domains that are non-overlapping with free poles on a circle

The thesis is devoted to the development of research methods of some well-known problems of the geometric function theory of a complex variable. In particular, we studied the problem, which V.\,N.~Dubinin had formulated in 1994 as an open problem. This problem is to find a maximum of the product of inner radii of $n$ mutually non-overlapping domains with respect to the points on a unit circle and the inner radius of positive degree $\gamma$ of the domain with respect to zero and description of extreme configurations. An attention in the dissertation is also given to the study of problem of maximizing the product of inner radii of non-overlapping domains in the case when some of the domains are symmetrical with respect to a unit circle.