Geodesic
Sharp estimates for functions with a~pole and a~logarithmic singularity
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2011), pp. 71-75.

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We consider functions with a pole and a logarithmic singularity. We obtain sharp estimates for the Schwarzian and the Taylor coefficients of the holomorphic part of such functions. We also describe geometric properties of conformal mappings of the exterior of the unit disc with a cut that connects some boundary point with a point at infinity.
Keywords: conformal mappings, Schwarzian
Mots-clés : coefficient estimates. 
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     title = {Sharp estimates for functions with a~pole and a~logarithmic singularity},
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}
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F. G. Avkhadiev. Sharp estimates for functions with a~pole and a~logarithmic singularity. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2011), pp. 71-75. http://geodesic.mathdoc.fr/item/IVM_2011_12_a8/

[1] Goluzin G. M., Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966 | MR | Zbl

[2] Pommerenke Ch., Univalent functions, Vandenhoeck and Ruprecht, Göttingen, 1975 | MR | Zbl

[3] Avkhadiev F. G., Aksentev L. A., “Osnovnye rezultaty v dostatochnykh usloviyakh odnolistnosti analiticheskikh funktsii”, UMN, 30:4 (1975), 3–60 | MR | Zbl

[4] Aksentev L. A., Avkhadiev F. G., “Ob odnom klasse odnolistnykh funktsii”, Izv. vuzov. Matem., 1970, no. 10, 12–20 | MR | Zbl

[5] Clunie J., “On meromorphic schlicht functions”, J. London Math. Soc., 34:2 (1959), 215–216 | DOI | MR | Zbl

[6] Pommerenke Ch., “On starlike and convex functions”, J. London Math. Soc., 37:146 (1962), 209–224 | DOI | MR | Zbl

[7] Avkhadiev F. G., Wirths K.-J., “Convex holes produce lower bounds for coefficients”, Complex Variables, 47:7 (2002), 553–563 | MR | Zbl

[8] Avkhadiev F. G., Pommerenke Ch., Wirths K.-J., “On the coefficients of concave univalent functions”, Math. Nachr., 271 (2004), 3–9 | DOI | MR | Zbl

[9] Avkhadiev F. G., Pommerenke Ch., Wirths K.-J., “Sharp inequalities for the coefficients of concave schlicht functions”, Comment. Math. Helv., 81:4 (2006), 801–807 | DOI | MR | Zbl

[10] Avkhadiev F. G., Wirths K.-J., “A proof of the Livingston conjecture”, Forum Math., 19 (2007), 149–157 | DOI | MR | Zbl

[11] Bhowmik B., Ponnusamy S., Wirths K.-J., “Domains of variability of Laurent coefficients and the convex hull for the family of concave univalent functions”, Kodai Math. J., 30:3 (2007), 385–393 | DOI | MR | Zbl

[12] Bkhoumik B., Ponnusami S., Virs K., “Vognutye funktsii, proizvedeniya Blyashke i poligonalnye otobrazheniya”, Sib. matem. zhurn., 50:4 (2009), 772–779 | MR

[13] Avkhadiev F. G., Wirths K.-J., Schwarz–Pick Type Inequalities, Birkhäuser, Basel–Boston–Berlin, 2009 | MR | Zbl

[14] Avkhadiev F. G., “Obratnaya kraevaya zadacha dlya funktsii s osobennostyami”, Tr. seminara po kraevym zadacham, 21, 1984, 5–19 | MR | Zbl

[15] Avkhadiev F. G., “Ob in'ektivnosti v oblasti otkrytykh izolirovannykh otobrazhenii s zadannymi granichnymi svoistvami”, DAN SSSR, 292:4 (1987), 780–783 | MR | Zbl