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
Scopus Publications
Scholar Citations
Scholar h-index
Scholar i10-index
Scopus Publications
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.
Iryna Denega
Springer International Publishing
Iryna Denega and Yaroslav Zabolotnyi
Odesa National University of Technology
In the paper we give a brief overview of the O. Bakhtin' scientific results
Aleksandr K. Bakhtin and Iryna V. Denega
Springer Science and Business Media LLC
Iryna Denega
Springer International Publishing
A. K. Bakhtin, L. V. Vyhivska, and I. V. Denega
Springer Science and Business Media LLC
Yaroslav Zabolotnii, , Iryna Denega, and
L. N. Gumilyov Eurasian National University
Ya. Zabolotnii and I. Denega
Petrozavodsk State University
A. K. Bakhtin and I. V. Denega
Springer Science and Business Media LLC
Aleksandr K. Bakhtin and Iryna V. Denega
Springer Science and Business Media LLC
Aleksandr K. Bakhtin and Iryna V. Denega
Springer Science and Business Media LLC
I. Denega
Petrozavodsk State University
A. K. Bakhtin and I. V. Denega
Springer Science and Business Media LLC
Iryna Denega
Springer Science and Business Media LLC
Yaroslav Zabolotnii and Iryna Denega
Springer Science and Business Media LLC
A. K. Bakhtin, I. V. Denega, and L. V. Vygovskaya
Springer Science and Business Media LLC
A. K. Bakhtin and I. V. Denega
Petrozavodsk State University
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.
Iryna V. Denega and Bogdan A. Klishchuk
Springer Science and Business Media LLC
A. K. Bakhtin, I. V. Denega, and Yu. V. Shunkin
Ivan Franko National University of Lviv
I. V. Denega and Ya. V. Zabolotnii
Informa UK Limited
This paper is devoted to one open extremal problem of Dubinin in geometric function theory of complex variables associated with estimates of a functional defined on the systems of non-overlapping domains. We consider Dubinin’s problem of the maximum of product of inner radii of n non-overlapping domains containing points of the unit circle and the power of the inner radius of a domain containing the origin. The problem was formulated in 1994 in the work of Dubinin and then repeated in his monograph in 2014. Currently it is not solved in general. In this paper, we obtained a solution of this problem for some concrete values of n and .
Irina Viktorovna Denega and Yaroslav Vladimirovich Zabolotnyi
Springer Science and Business Media LLC
A. Bakhtin, L. Vygivska, and I. Denega
Pleiades Publishing Ltd
Aleksandr K. Bakhtin, Liudmyla V. Vygivska, and Iryna V. Denega
Springer Science and Business Media LLC