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

• Autorzy: Iryna V. Denega
• 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.

Słowa kluczowe

EN

Extremal problems on non-overlapping domains; inner radius; n-radial system of points; separating transformation.

• Wydawca: Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
• Czasopismo: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
• Rocznik: 2013
• Tom: 67
• Numer: 1

Daty

wydano

2013

online

2015-07-15

Twórcy

autor

Iryna V. Denega

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).
• Duren, P. L., Univalent Functions, Springer-Verlag, New York, 1983.
• Goluzin, G. M., Geometric Theory of Functions of a Complex Variable, Translations of Mathematical Monographs, no. 26, Amer. Math. Soc., Providence, R.I. (1969).
• 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).
• Nehari, Z., Some inequalities in the theory of functions Trans. Amer. Math. Soc. 75, no. 2 (1953), 256–286.
• Riemann, B., Theorie der Abelschen Functionen J. Reine Angew. Math. 54 (1867), 101–155.
• Teichmuller, O., Collected Papers, Springer, Berlin, 1982.
• Vasil’ev, A., Moduli of Families of Curves for Conformal and Quasiconformal Mappings, Springer-Verlag, Berlin, 2002.

Identyfikatory

DOI

10.17951/a.2013.67.1.11-22