Geodesic
On the Univalence of an Integral on Subclasses of Meromorphic Functions
Matematičeskie zametki, Tome 69 (2001) no. 1, pp. 92-99.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the integral operator $P_\lambda[f](\zeta)=\int_{\zeta_0}^\zeta\bigl(f'(t)\bigr)^\lambda dt$, $|\zeta|>1$, acting on the class $\Sigma$ of functions meromorphic and univalent in the exterior of the unit disk. We refine the ranges of the parameter $\lambda$ for which the operator preserves univalence either on $\Sigma$ or on its subclasses consisting of convex functions. As a consequence, a two-sided estimate is deduced for the separating constant in the sufficient condition for the univalent solvability of exterior inverse boundary-value problems. 
@article{MZM_2001_69_1_a7,
     author = {I. R. Nezhmetdinov},
     title = {On the {Univalence} of an {Integral} on {Subclasses} of {Meromorphic} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {92--99},
     publisher = {mathdoc},
     volume = {69},
     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_69_1_a7/}
}
TY  - JOUR
AU  - I. R. Nezhmetdinov
TI  - On the Univalence of an Integral on Subclasses of Meromorphic Functions
JO  - Matematičeskie zametki
PY  - 2001
SP  - 92
EP  - 99
VL  - 69
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2001_69_1_a7/
LA  - ru
ID  - MZM_2001_69_1_a7
ER  - 
%0 Journal Article
%A I. R. Nezhmetdinov
%T On the Univalence of an Integral on Subclasses of Meromorphic Functions
%J Matematičeskie zametki
%D 2001
%P 92-99
%V 69
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2001_69_1_a7/
%G ru
%F MZM_2001_69_1_a7
I. R. Nezhmetdinov. On the Univalence of an Integral on Subclasses of Meromorphic Functions. Matematičeskie zametki, Tome 69 (2001) no. 1, pp. 92-99. http://geodesic.mathdoc.fr/item/MZM_2001_69_1_a7/

[1] Avkhadiev F. G., Aksentev L. A., Elizarov A. M., “Dostatochnye usloviya konechnolistnosti analiticheskikh funktsii i ikh prilozheniya”, Itogi nauki i tekhniki. Matematicheskii analiz, 25, VINITI, M., 1987, 3–121 | MR

[2] Pfaltzgraff J. A., “Univalence of the integral $\bigl (f'(z)\bigr )^\alpha $”, Bull. London Math. Soc., 7:3 (1975), 254–256 | DOI | MR | Zbl

[3] Royster W. C., “On the univalence of a certain integral”, Michigan Math. J., 12 (1965), 385–387 | DOI | MR | Zbl

[4] Aksentev L. A., Nezhmetdinov I. R., “Dostatochnye usloviya odnolistnosti nekotorykh integralnykh predstavlenii”, Trudy semin. po kraevym zadacham, 18, Izd-vo KGU, Kazan, 1982, 3–11

[5] Becker J., “Conformal mappings with quasiconformal extensions”, Aspects of Contemporary Complex Analysis, Academic Press, London, 1980, 37–72

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

[7] Avkhadiev F. G., “Ob usloviyakh odnolistnosti analiticheskikh funktsii”, Izv. vuzov. Matem., 1970, no. 11, 3–13 | MR | Zbl

[8] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady. Elementarnye funktsii, Nauka, M., 1981 | Zbl