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.
@article{bwmeta1.element.doi-10_2478_v10062-012-0018-9, author = {Iryna V. Denega}, title = {Generalization of some extremal problems on non-overlapping domains with free poles}, journal = {Annales UMCS, Mathematica}, volume = {67}, year = {2013}, pages = {11-22}, zbl = {1293.30055}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10062-012-0018-9} }
Iryna V. Denega. Generalization of some extremal problems on non-overlapping domains with free poles. Annales UMCS, Mathematica, Tome 67 (2013) pp. 11-22. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10062-012-0018-9/
[1] Bieberbach, L., ¨ Uber die Koeffizienten derjenigen Potenzreihen, welche eine schlichteAbbildung des Einheitskreises vermitteln, Sitzungsber. Preuss. Akad. Wiss. Phys- Math. Kl. 138 (1916), 940-955.
[2] Bakhtin, A. K., Bakhtina, G. P., Separating transformation and problem on nonoverlappingdomains, Proceedings of Institute of Mathematics of NAS of Ukraine 3 (4) (2006), 273-281. | Zbl 1199.30145
[3] Bakhtin, A. K., Bakhtina, G. P., Zelinskii, Yu. B., Topological-algebraic structures andgeometric methods in complex analysis, Proceedings of the Institute of Mathematics of NAS of Ukraine 73 (2008), 308 pp. (Russian). | Zbl 1199.30001
[4] Dubinin, V. N., The symmetrization method in problems on non-overlapping domains, Mat. Sb. (N.S.) 128 (1) (1985), 110-123 (Russian). | Zbl 0588.30024
[5] Dubinin, V. N., A separating transformation of domains and problems on extremaldecomposition, 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.
[6] Dubinin, V. N., Symmetrization method in geometric function theory of complexvariables, Uspekhi Mat. Nauk 49, no. 1 (1994), 3-76 (Russian); translation in Russian Math. Surveys 49, no. 1 (1994), 1-79.
[7] Dubinin, V. N., Asymptotics of the modulus of a degenerate condenser, and some ofits 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.
[8] Dubinin, V. N., Capacities of condensers and symmetrization in geometric functiontheory of complex variables, Dal’nayka, Vladivostok, 2009 (Russian).
[9] Duren, P. L., Univalent Functions, Springer-Verlag, New York, 1983.
[10] Goluzin, G. M., Geometric Theory of Functions of a Complex Variable, Translations of Mathematical Monographs, no. 26, Amer. Math. Soc., Providence, R.I. (1969). | Zbl 0183.07502
[11] Gr¨otzsch, H., ¨ Uber einige Extremalprobleme der konformen Abbildung. I, II, Ber. Verh. S¨achs. Akad. Wiss. Leipzig, Math.-Phys. 80 (6) (1928), 367-376, 497-502.
[12] Grunsky, H., Koeffizientenbedingungen f¨ur schlicht abbildende meromorphe Funltionen, Math. Z. 45, no. 1 (1939), 29-61. | Zbl 0022.15103
[13] Hayman, W. K., Multivalent Functions, Cambridge University Press, Cambridge, 1958.
[14] Jenkins, J. A., Some uniqueness results in the theory of symmetrization, Ann. Math. 61, no. 1 (1955), 106-115. | Zbl 0064.07501
[15] Kolbina, L. I., Conformal mapping of the unit circle onto non-overlapping domains, Vestnik Leningrad. Univ. 10, no. 5 (1955), 37-43 (Russian).
[16] Kovalev, L. V., On the problem of extremal decomposition with free poles on the circle, Dal’nevost. Mat. Sb. 2 (1996), 96-98 (Russian). | Zbl 0902.30018
[17] Lavrent’ev, M. A., On the theory of conformal mappings, Tr. Fiz.-Mat. Inst. Akad. Nauk SSSR, Otdel. Mat. 5 (1934), 195-245 (Russian).
[18] Nehari, Z., Some inequalities in the theory of functions Trans. Amer. Math. Soc. 75, no. 2 (1953), 256-286. | Zbl 0051.31204
[19] Riemann, B., Theorie der Abelschen Functionen J. Reine Angew. Math. 54 (1867), 101-155.
[20] Teichm¨uller, O., Collected Papers, Springer, Berlin, 1982.
[21] Vasil’ev, A., Moduli of Families of Curves for Conformal and Quasiconformal Mappings, Springer-Verlag, Berlin, 2002.