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Horowitz, David

Coefficient estimates for univalent polynomials. (English) Zbl 0347.30009

J. Anal. Math. 31, 112-124 (1977).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
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Cited in 1 Review
Cited in 3 Documents

MSC:

30C50 Coefficient problems for univalent and multivalent functions of one complex variable
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References:

[1] Bieberbach, L., Über die Koeffizienten derjenigen Potenzreihen, welche eine schlichte Abbildung des Einheitskreises vermitteln, K. Preuss. Wiss. Berlin, Sitzungsbereichte, 138, 940-955 (1916) · JFM 46.0552.01
[2] Dieudonné, J., Sur les fonctions univalentes, C. R. Acad. Sci. Ser. A, 192, 1148-1150 (1931) · Zbl 0001.34401
[3] Dieudonné, J., Recherches sur quelque problèmes relatifs aux polynomes et aux fonctions bornées d’une variable complexe, Ann. École Norm., 48, 3, 247-358 (1931) · JFM 57.0355.02
[4] FitzGerald, C., Quadratic inequalities and coefficient estimates for schlicht functions, Arch. Rational Mech. Anal., 46, 356-368 (1972) · Zbl 0242.30013 · doi:10.1007/BF00281102
[5] Garabedian, P.; Schiffer, M., A proof of the Bieberbach Conjecture for the fourth coefficient, J. Rat. Mech. Anal., 4, 427-465 (1955) · Zbl 0065.06902
[6] Horowitz, D., A refinement for coefficient estimates of univalent functions, Proc. Amer. Math. Soc., 54, 176-178 (1976) · Zbl 0294.30006 · doi:10.2307/2040778
[7] Loewner, K., Untersuchungen über schlichte konforme Abbildungen des Einkeitskreises, I, Math. Ann., 89, 103-121 (1923) · JFM 49.0714.01 · doi:10.1007/BF01448091
[8] Pederson, R., A proof of the Bieberbach Conjecture for the sixth coefficient, Arch. Rational Mech. Anal., 31, 331-351 (1968) · Zbl 0184.10501 · doi:10.1007/BF00251415
[9] Pederson, R.; Schiffer, M., A proof of the Bieberbach Conjecture for the fifth coefficient, Arch. Rational Mech. Anal., 45, 161-193 (1972) · Zbl 0241.30025 · doi:10.1007/BF00281531
[10] Rogosinski, W., Über positive harmonische Entwicklungen und typische realle Potenzreihen, Math. Z., 35, 93-121 (1932) · Zbl 0003.39303 · doi:10.1007/BF01186552
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