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Il’ina, L. P.

Estimates for the coefficients of univalent functions in terms of the second coefficient. (English) Zbl 0271.30015

Math. Notes 13, 215-218 (1973).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
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MSC:

30C50 Coefficient problems for univalent and multivalent functions of one complex variable
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[1] L. Bieberbach, ?über die Koeffizienten derjenigen Potenzreihen, welche schlichte Abbildung des Einheitskreises vermitteln,? Sitzgsber. Preuss. Akad. Wiss., Phys.-math. Kl.,138, 940-955 (1916). · JFM 46.0552.01
[2] K. Löwner, ?Untersuchungen über schlichte konforme Abbildungen des Einheitskreises,? Math. Ann.,89, 103-121 (1923). · JFM 49.0714.01 · doi:10.1007/BF01448091
[3] M. Schiffer and P. R. Garabedian, ?A proof of the Bieberbach conjecture for the fourth coefficient,? J. Rat. Mech. Anal.,4, No. 3, 427-465 (1955). · Zbl 0065.06902
[4] M. Schiffer and Z. Charzynski, ?A new proof of the Bieberbach conjecture for the fourth coefficient,? Arch. Rat. Mech. Anal.,5, No. 3, 187-193 (1960). · Zbl 0099.05901 · doi:10.1007/BF00252902
[5] R. N. Pederson, ?A proof of the Bieberbach conjecture for the sixth coefficient,? Arch. Rat. Mech. Anal.,31, No. 5, 331-351 (1968). · Zbl 0184.10501 · doi:10.1007/BF00251415
[6] G. G. Ross, P. R. Garabedian and M. Schiffer, ?On the Bieberbach conjecture for even n,? J. Math. Mech.,14, No. 6, 975-989 (1965). · Zbl 0141.26901
[7] P. R. Garabedian and M. Schiffer, ?The local maximum theorem for the coefficients of univalent functions,? Arch. Rat. Mech. Anal.,26, No. 1, 1-32 (1967). · Zbl 0174.12302 · doi:10.1007/BF00283856
[8] D. Aaronov, ?A proof of Bieberbach’s conjecture for a class of univalent functions,? Isr. J. Math.,8, No. 2, 103-104 (1970). · Zbl 0203.38402 · doi:10.1007/BF02771305
[9] I. M. Milin, Univalent Functions and Orthonormal Systems [in Russian], Moscow (1971).
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