Iryna Denega

RESEARCH, TEACHING, or OTHER INTERESTS

Analysis, Algebra and Number Theory

Scopus Publications

A note on conformal mappings onto mutually non-overlapping domains
Yaroslav Zabolotnyi and Iryna Denega
Walter de Gruyter GmbH
Abstract In the paper, an approach is proposed that allowed to establish new upper estimates for products of inner radii of mutually non-overlapping domains.


Using conformal radii of the open unit disk sectors in distortion theorems for univalent functions
Iryna Denega and Yaroslav Zabolotnyi
Springer Science and Business Media LLC



Inequalities for the Inner Radii of Domains Containing an Arbitrary Ellipse Points and Infinity
Iryna Denega and Yaroslav Zabolotnyi
Springer Nature Switzerland



On products of inner radii of non-overlapping domains containing certain segment points
Yaroslav Zabolotnyi and Iryna Denega
Informa UK Limited



Estimates of the functional with fixed points on hyperbola branches
Iryna Denega and Yaroslav Zabolotnyi
Odesa National University of Technology
In the paper an extreme problem of geometric function theory of a complex variable on the maximum of product of the inner radii on a system of n mutually non-overlapping multiply connected domains Bk containing the fixed points ak, k=1,...,n, located on a hyperbola branches is investigated.


ON THE PRODUCTS OF INNER RADII OF DOMAINS SATISFYING THE PARTIAL-INTERSECTION CONDITION
Iryna Denega and Yaroslav Zabolotnyi
Springer Science and Business Media LLC



On products of the inner radii of the domains containing points of some straight line
Iryna Denega and Yaroslav Zabolotnyi
Springer Science and Business Media LLC



Some extremal problems on the Riemannian sphere
I. Denega and Ya. V. Zabolotnyi

In the paper, the open problem of the maximum product of the inner radii of $n$ domains in the case, when points and domains belong to the unit circle, is investigated. This problem is solved only for $n=2$ and $n=3$. No other results are known at present. We obtain the result for all $n \\geqslant 2$. Also, we propose an approach that allows to establish evolutionary inequalities for the products of the inner radii of mutually non-overlapping domains.


On One Inequality for Non-overlapping Domains
Iryna Denega
Springer International Publishing



O. K. Bakhtin. Scientific legacy
Iryna Denega and Yaroslav Zabolotnyi
Odesa National University of Technology
In the paper we give a brief overview of the O. Bakhtin' scientific results


APPLICATION OF UPPER ESTIMATES FOR PRODUCTS OF INNER RADII TO DISTORTION THEOREMS FOR UNIVALENT FUNCTIONS
I. V. Denega and Ya. V. Zabolotnyi
Ivan Franko National University of Lviv
In 1934 Lavrentiev solved the problem of maximum ofproduct of conformal radii of two non-overlapping simply connected domains. In the case of three or more points, many authors considered estimates of a more general Mobius invariant of the form$$T_{n}:={\\prod\\limits_{k=1}^nr(B_{k},a_{k})}{\\bigg(\\prod\\limits_{1\\leqslant k<p\\leqslant n}|a_{k}-a_{p}|\\bigg)^{-\\frac{2}{n-1}}},$$where $r(B,a)$ denotes the inner radius of the domain $B$ with respect to the point $a$ (for an infinitely distant point under the corresponding factor we understand the unit).In 1951 Goluzin for $n=3$ obtained an accurate evaluation for $T_{3}$.In 1980 Kuzmina showedthat the problem of the evaluation of $T_{4}$ isreduced to the smallest capacity problem in the certain continuumfamily and obtained the exact inequality for $T_{4}$.No other ultimate results in this problem for $n \\geqslant 5$ are known at present.In 2021 \\cite{Bakhtin2021,BahDen22} effective upper estimates are obtained for $T_{n}$, $n \\geqslant 2$.Among the possible applications of the obtained results in other tasks of the function theory are the so-called distortion theorems.In the paper we consider an application of upper estimates for products of inner radii to distortion theorems for univalent functionsin disk $U$, which map it onto a star-shaped domains relative to the origin.


Generalized M.A. Lavrentiev’s inequality
Aleksandr K. Bakhtin and Iryna V. Denega
Springer Science and Business Media LLC



Extremal Decomposition of a Multidimensional Complex Space with Poles on the Boundary of a Polydisk
Iryna Denega
Springer International Publishing



Problem of Extreme Decomposition for a Complex Plane with Free Poles on a Circle
A. K. Bakhtin, L. V. Vyhivska, and I. V. Denega
Springer Science and Business Media LLC



Extremal Decomposition of the Complex Plane for n-Radial System of Points




About One Problem On Extremal Decomposition
Ya. Zabolotnii and I. Denega
Petrozavodsk State University



AN EXTREMAL PROBLEM ON NON-OVERLAPPING DOMAINS CONTAINING ELLIPSE POINTS
Yaroslav Zabolotnii, , Iryna Denega, and
L. N. Gumilyov Eurasian National University



Estimation of the Maximum Product of Inner Radii of Mutually Disjoint Domains
A. K. Bakhtin and I. V. Denega
Springer Science and Business Media LLC



Extremal Decomposition of the Complex Plane with Free Poles II
Aleksandr K. Bakhtin and Iryna V. Denega
Springer Science and Business Media LLC



Extremal decomposition of the complex plane with free poles
Aleksandr K. Bakhtin and Iryna V. Denega
Springer Science and Business Media LLC



Estimate of the maximum product of inner radii of non-overlapping domains
I. Denega
Petrozavodsk State University



Inequalities for the Inner Radii of Nonoverlapping Domains
A. K. Bakhtin and I. V. Denega
Springer Science and Business Media LLC



Estimates of the inner radii of non-overlapping domains
Iryna Denega
Springer Science and Business Media LLC



Extremal decomposition of a multidimensional complex space for five domains
Yaroslav Zabolotnii and Iryna Denega
Springer Science and Business Media LLC



Inequalities for the Inner Radii of Symmetric Disjoint Domains
A. K. Bakhtin, I. V. Denega, and L. V. Vygovskaya
Springer Science and Business Media LLC

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