http://dspace.nbuv.gov.ua:80/handle/123456789/169302 2026-04-16T10:27:35Z http://dspace.nbuv.gov.ua:80/handle/123456789/169415 Abstracts 2018-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/169414 Extremal decomposition of multidimensional complex space for five domains Zabolotni, i Y.; Denega, I. The paper is devoted to one open extremal problem in the geometric function theory of complex variables associated with estimates of a functional defined on the systems of non-overlapping domains. We consider the problem of the maximum of a product of inner radii of n non-overlapping domains containing points of a unit circle and the power γ of the inner radius of a domain containing the origin. The problem was formulated in 1994 in Dubinin’s paper in the journal “Russian Mathematical Surveys” in the list of unsolved problems and then repeated in his monograph in 2014. Currently, it is not solved in general. In this paper, we obtained a solution of the problem for five simply connected domains and power γ ∈ (1, 2.57] and generalized this result to the case of multidimensional complex space. 2018-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/169413 About one extremal problem for projections of the points on unit circle Targonskii, A.L. Sharp estimates of a product of inner radii for pairwise disjoint domains are obtained. In particular, the extremal problem in the case of any finite number of free poles at the points on rays is solved. 2018-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/169412 О локальном поведении одного класса обратных отображений Севостьянов, Е.А.; Скворцов, С.А. Изучены семейства отображений, обратные к которым удовлетворят неравенству типа Полецкого в заданной области. Доказано, что эти семейства равностепенно непрерывны во внутренних точках, если исходная и отображённая области ограничены, а мажоранта, отвечающая за искажение модуля, интегрируема. Если же исходная область локально связна на своей границе, а граница отображённой области является слабо плоской, соответствующие семейства отображений равностепенно непрерывны во внутренних и граничных точках.; We study the families of mappings such that the inverse ones satisfy an inequality of the Poletskii type in the given domain. It is proved that those families are equicontinuous at the inner points, if the initial and mapped domains are bounded, and the majorant responsible for a distortion of the modulus is integrable. But if the initial domain is locally connected on its boundary, and if the boundary of the mapped domain is weakly flat, then the corresponding families of mappings are equicontinuous at the inner and boundary points. 2018-01-01T00:00:00Z