Iryna Denega
@imath.kiev.ua
Complex analysis and potential theory department
Institute of mathematics of NAS of Ukraine
RESEARCH, TEACHING, or OTHER INTERESTS
Analysis, Algebra and Number Theory
29
Scopus Publications
376
Scholar Citations
10
Scholar h-index
11
Scholar i10-index
Scopus Publications
- 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 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 products of inner radii of non-overlapping domains containing certain segment points
Yaroslav Zabolotnyi and Iryna Denega
Informa UK Limited - 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. - 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 - 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
- AN EXTREMAL PROBLEM ON NON-OVERLAPPING DOMAINS CONTAINING ELLIPSE POINTS
Yaroslav Zabolotnii, , Iryna Denega, and
L. N. Gumilyov Eurasian National University - About One Problem On Extremal Decomposition
Ya. Zabolotnii and I. Denega
Petrozavodsk State 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 - Sharp estimates of products of inner radii of non-overlapping domains in the complex plane
A. K. Bakhtin and I. V. Denega
Petrozavodsk State University - Problem on extremal decomposition of the complex plane
Iryna Denega and Yaroslav Zabolotnii
Walter de Gruyter GmbH
Abstract In geometric function theory of a complex variable problems on extremal decomposition with free poles on the unit circle are well known. One of such problem is the problem on maximum of the functional r γ ( B 0 , 0 ) ∏ k = 1 n r ( B k , a k ) , $${r^\\gamma }({B_0},0)\\prod\\limits_{k = 1}^n r ({B_k},{a_k}),$$ where B 0, B 1, B 2,..., Bn, n ≥ 2, are pairwise disjoint domains in ¯, a 0 = 0, |ak| = 1, k = 1 , n ¯ $k = \\overline {1,n}$ and γ ∈ 2 (0; n], r(B, a) is the inner radius of the domain, B ⊂ ¯, with respect to a point a ∈ B. In the paper we consider a more general problem in which restrictions on the geometry of the location of points ak, k = 1 , n ¯ $k = \\overline {1,n}$ are weakened. - To the problem of extremal partition of the complex plane
Iryna V. Denega and Bogdan A. Klishchuk
Springer Science and Business Media LLC - Weakened problem on extremal decomposition of the complex plane
A. K. Bakhtin, I. V. Denega, and Yu. V. Shunkin
Ivan Franko National University of Lviv
RECENT SCHOLAR PUBLICATIONS
- Some extremal problems on the Riemannian sphere
IV Denega, YV Zabolotnyi
Carpathian Mathematical Publications 16 (2), 593-605 2024 - On products of inner radii of non-overlapping domains containing certain segment points
Y Zabolotnyi, I Denega
Complex Variables and Elliptic Equations, 1-14 2024 - On products of the inner radii of the domains containing points of some straight line
I Denega, Y Zabolotnyi
Journal of Mathematical Sciences 284 (3), 299-314 2024 - Application of upper estimates for products of inner radii to distortion theorems for univalent functions
IV Denega, YV Zabolotnyi
Matematychni Studii 60 (2), 138-144 2023 - Inequalities for the Inner Radii of Domains Containing an Arbitrary Ellipse Points and Infinity
I Denega, Y Zabolotnyi
ISAAC Congress (International Society for Analysis, its Applications and 2023 - AK Bakhtin. Scientific legacy
I Denega, Y Zabolotnyi
Proceedings of the International Geometry Center 16 (1), 1-16 2023 - with Poles on the Boundary of a Polydisk
I Denega
Current Trends in Analysis, its Applications and Computation: Proceedings of 2022 - Generalized MA Lavrentiev’s inequality
AK Bakhtin, IV Denega
Journal of Mathematical Sciences 262 (2), 138-153 2022 - Extremal decomposition of a multidimensional complex space with poles on the boundary of a polydisk
I Denega
Current Trends in Analysis, its Applications and Computation: Proceedings of 2021 - On One Inequality for Non-overlapping Domains
I Denega
ISAAC Congress (International Society for Analysis, its Applications and 2021 - Problem of Extreme Decomposition for a Complex Plane with Free Poles on a Circle.
AK Bakhtin, LV Vyhivska, IV Denega
Ukrainian Mathematical Journal 72 (12) 2021 - ISSUES OF ANALYSIS
YA ZABOLOTNII, I DENEGA
ISSUES OF ANALYSIS Учредители: Петрозаводский государственный университет 10 2021 - Extremal decomposition of the complex plane for n-radial system of points
I Denega
Azerbaijan Journal of Mathematics, Special Issue Dedicated to the 67th Birth 2021 - About one problem on extremal decomposition
YV Zabolotnii, IV Denega
Проблемы анализа—Issues of Analysis 10 (3), 141-150 2021 - An extremal problem on non-overlapping domains containing ellipse points
YV Zabolotnii, IV Denega
Eurasian Mathematical Journal 12 (4), 82-91 2021 - Задача про екстремальне розбиття комплексної площини з вільними полюсами на колі
OK Bakhtin, LV Vyhivska, IV Denega
Ukrains’ kyi Matematychnyi Zhurnal 72 (12), 1599-1620 2020 - Estimation of the Maximum Product of Inner Radii of Mutually Disjoint Domains.
AK Bakhtin, IV Denega
Ukrainian Mathematical Journal 72 (2), 191-203 2020 - Well-Posedness of a Mixed Problem in a Cylindrical Domain for One Class of Multidimensional Hyperbolic-Parabolic Equations.
SA Aldashev
Ukrainian Mathematical Journal 72 (2), 317-327 2020 - Estimate of maximum of the products of inner radii of mutually non-overlapping domains
I Denega
Algebraic and Geometric Methods of Analysis, 9 2020 - Extremal decomposition of the complex plane with free poles.
AK Bakhtin, IV Denega
Journal of Mathematical Sciences 246 (1), 1-18 2020
MOST CITED SCHOLAR PUBLICATIONS
- Extremal decomposition of the complex plane with free poles.
AK Bakhtin, IV Denega
Journal of Mathematical Sciences 246 (1), 1-18 2020
Citations: 36 - Addendum to a theorem on extremal decomposition of the complex plane
AK Bakhtin, IV Denega
Bulletin de la socit des sciences et des lettres de Łdź, Recherches sur 2012
Citations: 36 - Estimates of products of inner radii of non-overlapping domains in the complex plane
IV Denega, YV Zabolotnii
Complex Variables and Elliptic Equations 62 (11), 1611-1618 2017
Citations: 33 - Inequalities for the inner radii of nonorevlapping domains
AK Bakhtin, IV Denega
Ukrains’ kyi Matematychnyi Zhurnal 71 (7), 996-1002 2019
Citations: 26 - N-radial systems of points and problems for non-overlapping domains
A Bakhtin, L Vygivska, I Denega
Lobachevskii Journal of Mathematics 38, 229-235 2017
Citations: 23 - Estimates of the inner radii of non-overlapping domains
I Denega
Journal of Mathematical Sciences 242 (6), 787-795 2019
Citations: 18 - Inequalities for the internal radii of non-overlapping domains
AK Bakhtin, LV Vygivska, IV Denega
Journal of Mathematical Sciences 220 (5), 584 - 590. 2017
Citations: 15 - Generalization of some extremal problems on non-overlapping domains with free poles
IV Denega
Annales universitatis Mariae Curie-Skladovska, Lublin-Polonia 67 (1), 11 - 22 2013
Citations: extremal problems on non-overlapping domains with free poles - Generalization of some extremal problems on non-overlapping domains with free poles
IV Denega
2011
Citations: 15 - Generalized MA Lavrentiev’s inequality
AK Bakhtin, IV Denega
Journal of Mathematical Sciences 262 (2), 138-153 2022
Citations: 13 - Separating transformation and extremal decomposition of the complex plane
A Bakhtin, I Dvorak, I Denega
Bull. Soc. Sci. Lett. Ldz. Sr. Rech. Dform.–2016.–66, 13-20 2016
Citations: 12 - Некоторые оценки функционалов для N-лучевых систем точек
АК Бахтин, ИВ Денега
Зб. праць Ін-ту матем. НАН України 8 (№1), 12 – 21 2011
Citations: 10 - Inequality for the inner radii of symmetric non-overlapping domains
A Bakhtin, L Vyhivska, I Denega
Bulletin de la Socit des Sciences et des Lettres de Łdź 68 (2), 37-44 2018
Citations: 9 - Weakened problem on extremal decomposition of the complex plane
AK Bakhtin, IV Denega
Matematychni Studii 52 (1), 1-2 2019
Citations: 8 - Problem on extremal decomposition of the complex plane
I Denega, Y Zabolotnii
An. St. Univ. Ovidius Constanta 27 (1), 61-77 2019
Citations: 8 - About one Dubinin’s problem
AK Bakhtin, IV Denega
Proceedings of the Institute of Mathematics of NAS of Ukraine 10 (4-5), 401-411 2013
Citations: 8 - Квадратичные дифференциалы и разделяющее преобразование в экстремальных задачах о неналегающих областях
ИВ Денега
Доповіді НАН України, 15-19 2012
Citations: 8 - Sharp estimates of products of inner radii of non-overlapping domains in the complex plane
AK Bakhtin, IV Denega
Проблемы анализа 8 (1), 17-31 2019
Citations: 7 - Неравенства для внутренних радиусов неналегающих областей и открытых множеств
АК Бахтин, ИВ Денега
Укр. мат. журн 61, 596-610 2009
Citations: 7 - Separating transformation in a problem on extremal decomposition of the complex plane
I Denega, A Targonskii
Збірник Праць Інституту математики НАН України 14 (1), 147-155 2017
Citations: 6