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The growth of univalent functions with an initial gap II

Published online by Cambridge University Press:  10 April 2007

DOV AHARONOV  and
WALTER K. HAYMAN
DOV AHARONOV
Affiliation:
Department of Mathematics, Technion–Israel Institute of Technology, Haifa, 32000Israel. e-mail: dova@tx.technion.ac.il
WALTER K. HAYMAN
Affiliation:
Imperial College, London SW7 2AZ. e-mail: w.hayman@imperial.ac.uk
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Abstract

We consider the class Sp of functions univalent in the unit disk Δ.

In [1] it was shown that if f∈Sp and p is large, (0.1) Here we show that there exists f in Sp for p=1,2,. . . such that where C0 is a positive absolute constant.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 142 , Issue 2 , March 2007 , pp. 305 - 318
Copyright
Copyright © Cambridge Philosophical Society 2007

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References

REFERENCES

[1] Aharonov, D., Hayman, W. K. and Pommerenke, Ch.. The growth of univalent functions with an initial gap I. Math. Proc. Camb. Phil. Soc., 140 (2006), 305–312.CrossRefGoogle Scholar
[2] Duren, P. L.. Univalent Functions (Springer, 1983).Google Scholar
[3] Eremenko, A. and Hayman, W. K.. Univalent functions of fast growth with gap power series. Math. Proc. Camb. Phil. Soc. 127 (1999), 525–532.CrossRefGoogle Scholar
[4] Hayman, W. K.. Multivalent Functions (2nd edition) (Cambridge University Press, 1994).CrossRefGoogle Scholar
[5] Nehari, Z..Conformal Mapping (Mc Graw-Hill Book Company, 1952).Google Scholar