Extremal problems on the generalized (n, d)-equiangular system of points

Abstract

The paper of Lavrent'ev [1] was the beginning of geometrical theory of functions of the complex variable. He solved a problem on the product of conformal radiuses of two non-overlapping domains. In many papers (see [2] -[13]) the Lavrent'ev's result are generalized. In this paper are obtained the new results of this direction. A. TargonskiiLet N, R and C be the sets of natural, real and complex numbers respectively. We define C := C {∞} and R + := (0, ∞). Let n, m, d ∈ N such that m = nd. Consider the set of natural numbers(1)The following system of pointsare called the generalized (n, d)-equiangular system of points on the rays, if the condition (1) is fulfilled and if for all k = 1, n, p = 1, m k the following relations are true:

About one extremal problem for open sets and partially non-overlapping domains

“…In the last decade, Bakhtin's method of "managing functional" is actively used. A. K. Bakhtin solved a number of extremal problems for the so-called "radial systems of points" (see, e.g., [4,[7][8][9][10][11][12][13][14][15][16][17][18][19][20]). Namely this method will be applied in what follows.…”

An extremal problem for the nonoverlapping domains

“…In the last decade actively used Bakhtin's method of "managing functional". He managed to solve a series of extremal problems for so-called "radial systems of points" (see, e.g., [4,[7][8][9][10][11][12]). In the present paper we use the mentioned about Bakhtin's method.…”

A.K. Bakhtin. Scientific legacy

“…Under the O. K. Bakhtin supervision A. L. Targonskyi (2006) [12][13][14][41][42][43][44][45], V. E. Vyun (2008) [17][18][19], R. V. Podvisotskii [5,11], I. Y. Vygovska (2012) [46][47][48], I. V. Denega (2013) [7][8][9], Y. V. Zabolotnyi (2014) [20,22,26,27], L. V. Vyhivska (2019) [10,15,16], I. Y. Dvorak (2019) [10,21] defended their candidate theses.…”