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On Explicit Bounds In Landau's Theorem

Published online by Cambridge University Press:  20 November 2018

J. A. Jenkins
J. A. Jenkins*
Affiliation:
University of Notre Dame
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1. The theorem of Landau in question may be stated in the form that if the function F(Z) is regular for |Z| < 1 and does not take the values 0 and 1, while

F(Z) = a0 + a1Z + …

is its Taylor expansion about Z = 0, then |a1| has a bound depending only on a0. In fact |a1| has a bound depending only on |a0| and Hayman (1) gave the explicit bound

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 423 - 425
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Hayman, W. K., Some remarks on Schottky's Theorem, Proc. Cambridge Phil. Soc, 43 (1947), 442–454.Google Scholar
2. Jenkins, J. A., On explicit bounds in Schotiky's Theorem, Can. J. Math., 7 (1955), 76–82.Google Scholar
3. Robinson, R. M., Bounded univalent functions, Trans. Amer. Math. Soc, 52 (1942), 426–449.Google Scholar