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Extremal Problems on the Generalized (l, d)-Equiangular System Points in the Case of Arbitrary Multidimensional Complex Spaces

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Abstract:

In the paper we construct a counterpart of classical results on the generalized (l, d)-equiangular system points on the rays in the case of arbitrary multidimensional complex spaces.

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Periodical:
International Journal of Advanced Research in Mathematics (Volume 9)
Pages:
44-53
Citation:
A. L. Targonskii and I. Targonskaya, "Extremal Problems on the Generalized (l, d)-Equiangular System Points in the Case of Arbitrary Multidimensional Complex Spaces", International Journal of Advanced Research in Mathematics, Vol. 9, pp. 44-53, 2017
Online since:
June 2017
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[1] M.A. Lavrent'ev, On the theory of conformal mappings, Tr. Fiz. -Mat. Inst. Akad. Nauk SSSR. 5 (1934) 159-245. (in Russian).

[2] G.M. Goluzin, Geometric theory of functions of a complex variable, Nauka, Moscow, 1966. (in Russian).

[3] G.P. Bakhtina, Variational methods and quadratic differentials in problems for disjoint domains, PhD thesis, Kiev, Ukrainian SSR, 1975. (in Russian).

[4] A.K. Bakhtin, G.P. Bakhtina, Yu.B. Zelinskii, Topological-algebraic structures and geometric methods in complex analysis, Inst. Math. NAS Ukraine, Kiev, Ukraine, 2008. (in Russian).

[5] V.N. Dubinin Separating transformation of domains and problems of extremal division, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Ros. Akad. Nauk. 168 (1988) 48-66. (in Russian).

[6] V.N. Dubinin, Method of symmetrization in the geometric theory of functions of a complex variable, Usp. Mat. Nauk. 49(1) (1994) 3-76.

[7] A.K. Bakhtin, Inequalities for the inner radii of nonoverlapping domains and open sets, Ukr. Math. J. 61(5) (2009) 716-733.

DOI: https://doi.org/10.1007/s11253-009-0247-4

[8] A.K. Bakhtin, A.L. Targonskii, Extremal problems and quadratic differential, Nonlin. Oscillations. 8(3) (2005) 296-301.

[9] A.K. Bakhtin, A.L. Targonskii, Generalized (n, d)-ray systems of points and inequalities for nonoverlapping domains and open sets, Ukr. Math. J. 63(7) (2011) 999-1012.

DOI: https://doi.org/10.1007/s11253-011-0560-6

[10] S.A. Ochrimenko, , A.L. Targonskii, Extreme problems for generalized ray systems of points, Zb. Praz. Ins-tu Matemat. NAN Ukrainy. 9(2) (2012) 270-284. (in Russian).

[11] A. Targonskii, Extremal problems on the generalized (n; d)-equiangular system of points, An. St. Univ. Ovidius Constanta. 22(2) (2014) 239-251.

DOI: https://doi.org/10.2478/auom-2014-0044

[12] A.L. Targonskii, Extremal problems for partially non-overlapping domains on equiangular systems of points, Bull. Soc. Sci. Lett. Lodz. 63(1) (2013) 57-63.

[13] A. Targonskii, I. Targonskaya, On the one extremal problem on the Riemann sphere, International Journal of Advanced Research in Mathematics. 4 (2016) 1-7.

DOI: https://doi.org/10.18052/www.scipress.com/ijarm.4.1

[14] A.K. Bakhtin, Analytic functions of vector argument and partially-conformal mappings in multidimensional complex spaces, in: Progress in Analysis, Proceedings of the 8th Congress of the International Society for Analysis, its Applications, and Computation, 2011, pp.1-8.

[15] A.K. Bakhtin, The generalization of some results of the theory of univalent functions on multidimensional complex spaces, Dop. NAN Ukr. 3 (2011) 7-11. (in Russian).

[16] Ya.V. Zabolotnyi, On one Dubinin extreme problem, Ukr. Math. J. 64(1) (2012) 24-34.

DOI: https://doi.org/10.1007/s11253-012-0627-z

[17] V.N. Dubinin, Asymptotic representation of the modulus of a degenerating condenser and some its applications, Zap. Nauchn. Sem. Peterburg. Otdel. Mat. Inst. 237 (1997) 56-73. (in Russian).

[18] V.N. Dubinin, Capacities of condensers and symmetrization in geometric function theory of complex variables, Dal'nayka, Vladivostok, Russia, 2009. (in Russian).

[19] W.K. Hayman, Multivalent functions, Cambridge University, Cambridge, (1958).

[20] J.A. Jenkins, Univalent functions and conformal mapping, Springer, Berlin, (1958).

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