Geodesic
Inequalities for the Schwarzian derivative for subclasses of convex functions in the unit disc
Vladikavkazskij matematičeskij žurnal, Tome 8 (2006) no. 2, pp. 50-53 
Y. Polatoglu; M. Caglar; A. Sen. Inequalities for the Schwarzian derivative for subclasses of convex functions in the unit disc. Vladikavkazskij matematičeskij žurnal, Tome 8 (2006) no. 2, pp. 50-53. http://geodesic.mathdoc.fr/item/VMJ_2006_8_2_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Nehari norm of the Schwarzian derivative of an analytic function is closely related to its univalence. The famous Nehari-Kraus theorem ([3], [4]) and Ahlfors-Weill theorem [1] are of fundamental importance in this direction. For a non-constant meromorphic function $f$ on $D$ the unite disc, the Schwarzian derivative $S_f$ of $f$ by is holomorphic at $z_0\in D$ if and only if $f$ is locally univalent at $z_0$. The aim of this paper is to give sharp estimates of the Nehari norm for the subclasses of convex functions in the unit disc.

[1] Duren P. L., Univalent Functions, Springer-Verlag New York Inc., NY, 1983 | MR | Zbl

[2] Janowski W., “Some Extremal Problems for Certain Families of Analytic Functions, I”, Annales Polinici Math., 28 (1973), 297–326 | MR | Zbl

[3] Kraus W., “Über den Zusammanhang Charakteristiken Eines Einfach Zusammeshängenden Bereiches mit der Kreisabbildung”, Mitt. Math. Sem. Giessen, 21 (1932), 1–28 | Zbl

[4] Nehari Z., “The Schwarzian Derivative and Schlicht Functions”, Bull. Amer. Math. Soc., 55 (1949), 445–551 | DOI | MR

[5] Robertson M. S., “Univalent Functions for which $zf'(z)$ is spirallike”, Michigan Math. J., 16 (1969), 97–101 | DOI | MR | Zbl