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Subordination by convex functions. (English) Zbl 0311.30010


MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C75 Extremal problems for conformal and quasiconformal mappings, other methods
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References:

[1] L. Brickman, D. J. Hallenbeck, T. H. MacGregor, and D. R. Wilken, Convex hulls and extreme points of families of starlike and convex mappings, Trans. Amer. Math. Soc. 185 (1973), 413 – 428 (1974). · Zbl 0278.30021
[2] C. Carathéodory, Funktionentheorie, Band 2, Birkhäuser, Basel, 1950; English transl., Chelsea, New York, 1954. MR 12, 248; 16, 346.
[3] D. J. Hallenbeck, Convex hulls and extreme points of some families of univalent functions, Trans. Amer. Math. Soc. 192 (1974), 285 – 292. · Zbl 0296.30014
[4] I. S. Jack, Functions starlike and convex of order \?, J. London Math. Soc. (2) 3 (1971), 469 – 474. · Zbl 0224.30026
[5] Stephan Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109 – 115. · Zbl 0303.30006
[6] St. Ruscheweyh and T. Sheil-Small, Hadamard products of Schlicht functions and the Pólya-Schoenberg conjecture, Comment. Math. Helv. 48 (1973), 119 – 135. · Zbl 0261.30015
[7] Erich Strohhäcker, Beiträge zur Theorie der schlichten Funktionen, Math. Z. 37 (1933), no. 1, 356 – 380 (German). · Zbl 0007.21402
[8] D. Styer and D. Wright, On the valence of the sum of two convex functions, Proc. Amer. Math. Soc. 37 (1973), 511 – 516. · Zbl 0262.30008
[9] T. J. Suffridge, Some remarks on convex maps of the unit disk, Duke Math. J. 37 (1970), 775 – 777. · Zbl 0206.36202
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