Geodesic
Covering Theorems for Classes of Univalent Functions
Canadian journal of mathematics, Tome 25 (1973) no. 2, pp. 412-419

Voir la notice de l'article provenant de la source Cambridge University Press

Let denote the class of functions f(z) = z + that are analytic and univalent in and will denote the collection of f ∈ that map U onto a domain that is respectively starlike with respect to the origin and convex.In [4, p. 85] Hayman used Steiner symmetrization to solve a problem, a special case of which is the following. 
Aharonov, Dov; Kirwan, W. E. Covering Theorems for Classes of Univalent Functions. Canadian journal of mathematics, Tome 25 (1973) no. 2, pp. 412-419. doi: 10.4153/CJM-1973-041-9
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[1] 1. Aharonov, D. and Kirwan, W. E., A method of symmetrization and applications, Trans Amer. Math. Soc. (to appear). Google Scholar

[2] 2. Aharonov, D. and Kirwan, W. E., A method of symmetrization and applications, II (to appear). Google Scholar

[3] 3. Frantz, W. and Kratzer, A., Tranzendente Functionen (Akademische Verlagsgesellschaft, Leipzig, 1960). Google Scholar

[4] 4. Hayman, W. K., Multivalent functions (Cambridge University Press, Cambridge, 1958). Google Scholar

[5] 5. Jenkins, J. A., On values omitted by univalent functions, Amer. J. Math. 2 (1953), 406–408. Google Scholar

[6] 6. Klein, M., Estimates for the transfinite diameter with applications to conformai mapping, Pacific J. Math. 22 (1967), 267–279. Google Scholar

[7] 7. Lewandowski, Z., On circular symmetrization of starlike functions, Ann. Univ. Mariae Curie-Sklodowska Sect. A 17 (1963), 35–37. Google Scholar

[8] 8. Löwner, K., Untersuchengen über die Verzerrung bei konformen Abbildungen des Einheitskreises, die durch Functionen mit nicht Verschwindender Ableitung geliefert werden, Berichte Könige. Sachs. Ges. Wissen, Leipzig 69 (1917), 89–106. Google Scholar

[9] 9. Nehari, Z., Conformai mapping (McGraw-Hill, New York, 1952). Google Scholar

[10] 10. Strohhäcker, E., Beiträgezur Théorie der Schlichten Functionen, Math. Z. 37 (1933), 356–380. Google Scholar

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