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On the coefficient problem for univalent polynomials

Published online by Cambridge University Press:  24 October 2008

Julian Ławrynowicz
Julian Ławrynowicz
Affiliation:
Institute of Mathematics of the Polish Academy of Sciences Laboratory in Łódz
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Extract

This paper is concerned with estimates of the coefficients Cn for normalized polynomials, inverse to univalent functions in the unit disc, i.e. univalent polynomials of the form

considered in the largest domain D such that 0 ∈ D and |pn(w)| < 1 for w ∈ D; this domain will be denoted by . Polynomials of the type (1) have been introduced by Charzyński in (1), where it was proved among other results that the domain is simply connected.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 1 , January 1968 , pp. 87 - 98
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

(1)Charzyński, Z.Fonctions univalentes inverses. Polynomes univalentes. Bull. Soc. Sci. Lettres Łódź. 97 (1958), 1–21.Google Scholar
(2)Charzyński, Z.and Ławbytstowicz, J. On the coefficients of univalent polynomials. Colloq. Math. 16 (1967), 27–33.CrossRefGoogle Scholar
(3)Löwner, K.Untersuchungen über schlichte konforme Abbildimgen des Einheitskreises I. Math. Ann. 89 (1923), 103–121.CrossRefGoogle Scholar