A note on conformal mappings onto mutually non-overlapping domains Yaroslav Zabolotnyi, Iryna Denega Analele Stiintifice Ale Universitatii Ovidius Constanta Seria Matematica, 2025 In the paper, an approach is proposed that allowed to establish new upper estimates for products of inner radii of mutually non-overlapping domains.
Estimates of the functional with fixed points on hyperbola branches Iryna Denega, Yaroslav Zabolotnyi Proceedings of the International Geometry Center, 2025 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.
Estimates for sums of logarithmic potentials associated with the Green function I. Denega, Ya. Zabolotnyi Researches in Mathematics, 2025 This article presents a study on the analytical solution of the Dirichlet problem for the Laplace equation in two-dimensional space. The primary focus is on the Green's function, which is a key tool for solving such problems. We considered cases where the sources are located on geometrically simple sets: on a straight line, a unit circle, and a line segment.We developed and applied an effective method for calculating the sum of harmonic functions $h_k(z,a_k)$, which are the correcting terms in the Green's function expression. This allowed us to obtain analytical formulas for the potential generated by a system of point sources located in the specified configurations. Specifically, for each case, we found an estimate for the total potential.The findings are of significant value to theoretical physics and engineering applications, particularly in electrostatics, heat conduction, and hydrodynamics, where similar boundary value problems arise. The proposed approach can serve as a basis for further research aimed at solving more complex problems with sources located on curved or higher-dimensional manifolds.
Some extremal problems on the Riemannian sphere I. Denega, Ya. V. Zabolotnyi Carpathian Mathematical Publications, 2024 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.
Estimates for sums of logarithmic potentials associated with the Green function I Denega, Y Zabolotnyi Researches in Mathematics 33 (3), 14-22 , 2025 2025
On the products of inner radii of domains satisfying the partial-intersection condition I Denega, Y Zabolotnyi Journal of Mathematical Sciences 294 (5), 651-668 , 2025 2025
On products of inner radii of non-overlapping domains containing certain segment points Y Zabolotnyi, I Denega Complex Variables and Elliptic Equations 70 (9), 1584-1597 , 2025 2025 Citations: 2
Using conformal radii of the open unit disk sectors in distortion theorems for univalent functions I Denega, Y Zabolotnyi Complex Analysis and its Synergies 11 (2), 8 , 2025 2025 Citations: 2
Estimates of the functional with fixed points on hyperbola branches. Y Zabolotnyi, I Denega Proceedings of the International Geometry Center 18 (2) , 2025 2025
A note on conformal mappings onto mutually non-overlapping domains Z Yaroslav, D Iryna Analele Stiintifice ale Universitatii" Ovidius" Constanta. Seria Matematica … , 2025 2025
Some extremal problems on the Riemannian sphere IV Denega, YV Zabolotnyi Carpathian Mathematical Publications 16 (2), 593-605 , 2024 2024 Citations: 4
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 2024 Citations: 4
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 2023 Citations: 16
On One Inequality for Non-overlapping I Denega Analysis, Applications, and Computations: Proceedings of the 13th ISAAC … , 2023 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 2023 Citations: 1
OK Bakhtin. Scientific legacy. I Denega, Y Zabolotnyi Proceedings of the International Geometry Center 16 (1) , 2023 2023
with Poles on the Boundary of a Polydisk I Denega Current Trends in Analysis, its Applications and Computation: Proceedings of … , 2022 2022
Generalized MA Lavrentiev’s inequality AK Bakhtin, IV Denega Journal of Mathematical Sciences 262 (2), 138-153 , 2022 2022 Citations: 24
An extremal problem on non-overlapping domains containing ellipse points Y Zabolotnii, I Denega Eurasian Mathematical Journal 12 (4), 82-91 , 2021 2021 Citations: 6
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 2021 Citations: 1
On One Inequality for Non-overlapping Domains I Denega ISAAC Congress (International Society for Analysis, its Applications and … , 2021 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 2021 Citations: 4
ISSUES OF ANALYSIS YA ZABOLOTNII, I DENEGA ISSUES OF ANALYSIS Учредители: Петрозаводский государственный университет 10 … , 2021 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 2021 Citations: 3
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 2020 Citations: 46
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 2017 Citations: 44
Addendum to a theorem on extremal decomposition of the complex plane AK Bakhtin, IV Denega Bulletin de la société des sciences et des lettres de Łódź, Recherches sur … , 2012 2012 Citations: 40
Inequalities for the inner radii of nonorevlapping domains AK Bakhtin, IV Denega Ukrains’ kyi Matematychnyi Zhurnal 71 (7), 996-1002 , 2019 2019 Citations: 33
N -radial systems of points and problems for non-overlapping domains A Bakhtin, L Vygivska, I Denega Lobachevskii Journal of Mathematics 38 (2), 229-235 , 2017 2017 Citations: 25
Generalized MA Lavrentiev’s inequality AK Bakhtin, IV Denega Journal of Mathematical Sciences 262 (2), 138-153 , 2022 2022 Citations: 24
Estimates of the inner radii of non-overlapping domains I Denega Journal of Mathematical Sciences 242 (6), 787-795 , 2019 2019 Citations: 23
Inequalities for the internal radii of non-overlapping domains AK Bakhtin, LV Vygivska, IV Denega Journal of Mathematical Sciences 220 (5), 584 - 590. , 2017 2017 Citations: 18
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 2013 Citations: 18
Generalization of some extremal problems on non-overlapping domains with free poles IV Denega 2011 Citations: 18
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 2023 Citations: 16
Неравенства для внутренних радиусов неналегающих областей AК Бахтин, ЛВ Выговская, ИВ Денега Український математичний вісник, 68-75 , 2016 2016 Citations: 15
Неравенства для внутренних радиусов неналегающих областей АК Бахтин, ЛВ Выговская, ИВ Денега Український математичний вiсник 13 (1), 68 – 75. , 2016 2016 Citations: 15
Separating transformation and extremal decomposition of the complex plane A Bakhtin, I Dvorak, I Denega Bull. Soc. Sci. Lett. Lódz. Sér. Rech. Déform.–2016.–66, 13-20 , 2016 2016 Citations: 14
Problem on extremal decomposition of the complex plane I Denega, Y Zabolotnii An. St. Univ. Ovidius Constanta 27 (1), 61-77 , 2019 2019 Citations: 12
Inequality for the inner radii of symmetric non-overlapping domains A Bakhtin, L Vyhivska, I Denega Bulletin de la Société des Sciences et des Lettres de Łódź, Série … , 2018 2018 Citations: 11
Некоторые оценки функционалов для N-лучевых систем точек АК Бахтин, ИВ Денега Зб. праць Ін-ту матем. НАН України 8 (№1), 12 – 21 , 2011 2011 Citations: 11
Weakened problem on extremal decomposition of the complex plane AK Bakhtin, IV Denega Matematychni Studii 52 (1), 1-2 , 2019 2019 Citations: 10
Об одной проблеме В. Н. Дубинина АК Бахтин, ИВ Денега Зб. праць Ін-ту матем. НАН України 10 (4-5), 401 – 411 , 2013 2013 Citations: 9
Квадратичные дифференциалы и разделяющее преобразование в экстремальных задачах о неналегающих областях ИВ Денега Доповіді НАН України, 15-19 , 2012 2012 Citations: 9