Geodesic
On the Jenkins covering circle theorem for holomorphic functions in a disk
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 28, Tome 418 (2013), pp. 60-73 
V. N. Dubinin. On the Jenkins covering circle theorem for holomorphic functions in a disk. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 28, Tome 418 (2013), pp. 60-73. http://geodesic.mathdoc.fr/item/ZNSL_2013_418_a3/
@article{ZNSL_2013_418_a3,
     author = {V. N. Dubinin},
     title = {On the {Jenkins} covering circle theorem for holomorphic functions in a~disk},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {60--73},
     year = {2013},
     volume = {418},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_418_a3/}
}
TY  - JOUR
AU  - V. N. Dubinin
TI  - On the Jenkins covering circle theorem for holomorphic functions in a disk
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2013
SP  - 60
EP  - 73
VL  - 418
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2013_418_a3/
LA  - ru
ID  - ZNSL_2013_418_a3
ER  - 
%0 Journal Article
%A V. N. Dubinin
%T On the Jenkins covering circle theorem for holomorphic functions in a disk
%J Zapiski Nauchnykh Seminarov POMI
%D 2013
%P 60-73
%V 418
%U http://geodesic.mathdoc.fr/item/ZNSL_2013_418_a3/
%G ru
%F ZNSL_2013_418_a3

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The well-known Jenkins' theorem on values omitted by univalent functions is extended for some meromorphic $p$-valent functions in the unit disk. The multiplicity of the function covering and the values of the functions in the critical points is taken into account.

[1] J. A. Jenkins, “On values omitted by univalent functions”, Amer. J. Math., 75 (1953), 406–408 | DOI | MR | Zbl

[2] G. M. Goluzin, Geometricheskaya teoriya funktsii kompleksnogo peremennogo, M., 1966

[3] G. Polia, G. Sege, Izoperimetricheskie neravenstva v matematicheskoi fizike, M., 1962 | MR

[4] T. Kubo, “Symmetrization and univalent functions in an annulus”, J. Math. Soc. Japan, 6 (1954), 55–67 | DOI | MR | Zbl

[5] S. Sato, “Dve teoremy ob ogranichennykh funktsiyakh”, Sugaku, 7 (1955), 99–101

[6] S. Sato, “O znacheniyakh, ne prinimaemykh ogranichennymi odnolistnymi funktsiyami”, Kenkyu khokoku. Sidzen Kachaku. Liberal Arts J. Natur. Sci., 6 (1955), 1–6

[7] A. W. Goodman, E. Reich, “On regions omitted by univalent functions. II”, Canad. J. Math., 7 (1955), 83–88 | DOI | MR | Zbl

[8] M. I. Revyakov, “O znacheniyakh, ne prinimaemykh odnolistnymi funktsiyami”, Tr. Mat. in-ta im. V. A. Steklova, 94, 1968, 123–129 | MR | Zbl

[9] A. Yu. Solynin, Nekotorye otsenki dlya regulyarnykh funktsii, vypuskayuschikh znacheniya na okruzhnosti, Deponirovano v VINITI No 2016–83, Kubanskii gos. un-t, Krasnodar, 1983, 17 pp.

[10] Dzh. Dzhenkins, Odnolistnye funktsii i konformnye otobrazheniya, M., 1962

[11] V. N. Dubinin, “Novaya versiya krugovoi simmetrizatsii s prilozheniyami k $p$-listnym funktsiyam”, Mat. sb., 203:7 (2012), 79–94 | DOI | MR | Zbl

[12] W. K. Hayman, Multivalent functions, Second ed., Cambridge Univ. Press, Cambridge, 1994 | MR | Zbl

[13] A. Gurvits, R. Kurant, Teoriya funktsii, M., 1968

[14] V. N. Dubinin, “Simmetrizatsiya v geometricheskoi teorii funktsii kompleksnogo peremennogo”, Uspekhi mat. nauk, 49:1 (1994), 3–76 | MR | Zbl

[15] I. P. Mityuk, Simmetrizatsionnye metody i ikh primenenie v geometricheskoi teorii funktsii. Vvedenie v simmetrizatsionnye metody, Kubanskii gos. un-t, Krasnodar, 1980

[16] V. N. Dubinin, “O prinitsipakh mazhoratsii dlya meromorfnykh funktsii”, Mat. zametki, 84:6 (2008), 803–808 | DOI | MR | Zbl