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Support points of families of analytic functions described by subordination. (English) Zbl 0521.30018


MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination
30D50 Blaschke products, etc. (MSC2000)
30C70 Extremal problems for conformal and quasiconformal mappings, variational methods
30C75 Extremal problems for conformal and quasiconformal mappings, other methods
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References:

[1] Yusuf Abu-Muhanna and Thomas H. MacGregor, Extreme points of families of analytic functions subordinate to convex mappings, Math. Z. 176 (1981), no. 4, 511 – 519. · Zbl 0461.30018
[2] D. A. Brannan, J. G. Clunie, and W. E. Kirwan, On the coefficient problem for functions of bounded boundary rotation, Ann. Acad. Sci. Fenn. Ser. A I 523 (1973), 18. · Zbl 0257.30011
[3] L. Brickman, T. H. MacGregor, and D. R. Wilken, Convex hulls of some classical families of univalent functions, Trans. Amer. Math. Soc. 156 (1971), 91 – 107. · Zbl 0227.30013
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[8] Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962. · Zbl 0734.46033
[9] Thomas H. MacGregor, Applications of extreme-point theory to univalent functions, Michigan Math. J. 19 (1972), 361 – 376. · Zbl 0257.30017
[10] Werner Rogosinski, On the coefficients of subordinate functions, Proc. London Math. Soc. (2) 48 (1943), 48 – 82. · Zbl 0028.35502
[11] Glenn Schober, Univalent functions — selected topics, Lecture Notes in Mathematics, Vol. 478, Springer-Verlag, Berlin-New York, 1975. · Zbl 0306.30018
[12] T. J. Suffridge, Some remarks on convex maps of the unit disk, Duke Math. J. 37 (1970), 775 – 777. · Zbl 0206.36202
[13] Otto Toeplitz, Die linearen vollkommenen Räume der Funktionentheorie, Comment. Math. Helv. 23 (1949), 222 – 242 (German). · Zbl 0035.07301
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