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

Annales UMCS, Mathematica (2013)

- Volume: 67, Issue: 1, page 11-22
- ISSN: 2083-7402

## Access Full Article

top## Abstract

top## How to cite

topIryna V. Denega. "Generalization of some extremal problems on non-overlapping domains with free poles." Annales UMCS, Mathematica 67.1 (2013): 11-22. <http://eudml.org/doc/267910>.

@article{IrynaV2013,

abstract = {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.},

author = {Iryna V. Denega},

journal = {Annales UMCS, Mathematica},

keywords = {Extremal problems on non-overlapping domains; inner radius; n-radial system of points; separating transformation; extremal problems on non-overlapping domains; -radial system of points},

language = {eng},

number = {1},

pages = {11-22},

title = {Generalization of some extremal problems on non-overlapping domains with free poles},

url = {http://eudml.org/doc/267910},

volume = {67},

year = {2013},

}

TY - JOUR

AU - Iryna V. Denega

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

JO - Annales UMCS, Mathematica

PY - 2013

VL - 67

IS - 1

SP - 11

EP - 22

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/267910

ER -

## References

top- [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. Zbl1199.30145
- [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). Zbl1199.30001
- [4] Dubinin, V. N., The symmetrization method in problems on non-overlapping domains, Mat. Sb. (N.S.) 128 (1) (1985), 110-123 (Russian). Zbl0588.30024
- [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). Zbl0183.07502
- [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. Zbl0022.15103
- [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. Zbl0064.07501
- [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). Zbl0902.30018
- [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. Zbl0051.31204
- [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.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.