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2013 | 67 | 1 |
Tytuł artykułu

Generalization of some extremal problems on non-overlapping domains with free poles

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Some results related to extremal problems with free poles on radial systems are generalized. They are obtained by applying the known methods of geometric function theory of complex variable. Sufficiently good numerical results for γ are obtained.
Rocznik
Tom
67
Numer
1
Opis fizyczny
Daty
wydano
2013
online
2015-07-15
Twórcy
Bibliografia
  • Bieberbach, L., Uber die Koeffizienten derjenigen Potenzreihen, welche eine schlichte Abbildung des Einheitskreises vermitteln, Sitzungsber. Preuss. Akad. Wiss. Phys-Math. Kl. 138 (1916), 940–955.
  • Bakhtin, A. K., Bakhtina, G. P., Separating transformation and problem on nonoverlapping domains, Proceedings of Institute of Mathematics of NAS of Ukraine 3 (4) (2006), 273–281.
  • Bakhtin, A. K., Bakhtina, G. P., Zelinskii, Yu. B., Topological-algebraic structures and geometric methods in complex analysis, Proceedings of the Institute of Mathematics of NAS of Ukraine 73 (2008), 308 pp. (Russian).
  • Dubinin, V. N., The symmetrization method in problems on non-overlapping domains, Mat. Sb. (N.S.) 128 (1) (1985), 110–123 (Russian).
  • Dubinin, V. N., A separating transformation of domains and problems on extremal decomposition, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 168 (1988), 48–66 (Russian); translation in J. Soviet Math. 53, no. 3 (1991), 252–263.
  • Dubinin, V. N., Symmetrization method in geometric function theory of complex variables, Uspekhi Mat. Nauk 49, no. 1 (1994), 3–76 (Russian); translation in Russian Math. Surveys 49, no. 1 (1994), 1–79.
  • Dubinin, V. N., Asymptotics of the modulus of a degenerate condenser, and some of its applications, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 237 (1997), 56–73 (Russian); translation in J. Math. Sci. (New York) 95, no. 3 (1999), 2209–2220.
  • Dubinin, V. N., Capacities of condensers and symmetrization in geometric function theory of complex variables, Dal’nayka, Vladivostok, 2009 (Russian).
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  • Grotzsch, H., Uber einige Extremalprobleme der konformen Abbildung. I, II, Ber. Verh. Sachs. Akad. Wiss. Leipzig, Math.-Phys. 80 (6) (1928), 367–376, 497–502.
  • Grunsky, H., Koeffizientenbedingungen f¨ur schlicht abbildende meromorphe Funltionen, Math. Z. 45, no. 1 (1939), 29–61.
  • Hayman, W. K., Multivalent Functions, Cambridge University Press, Cambridge, 1958.
  • Jenkins, J. A., Some uniqueness results in the theory of symmetrization, Ann. Math. 61, no. 1 (1955), 106–115.
  • Kolbina, L. I., Conformal mapping of the unit circle onto non-overlapping domains, Vestnik Leningrad. Univ. 10, no. 5 (1955), 37–43 (Russian).
  • Kovalev, L. V., On the problem of extremal decomposition with free poles on the circle, Dal’nevost. Mat. Sb. 2 (1996), 96–98 (Russian).
  • Lavrent’ev, M. A., On the theory of conformal mappings, Tr. Fiz.-Mat. Inst. Akad. Nauk SSSR, Otdel. Mat. 5 (1934), 195–245 (Russian).
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  • Vasil’ev, A., Moduli of Families of Curves for Conformal and Quasiconformal Mappings, Springer-Verlag, Berlin, 2002.
Typ dokumentu
Bibliografia
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bwmeta1.element.ojs-doi-10_17951_a_2013_67_1_11-22
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