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Coefficient regions for univalent polynomials of small degree

Published online by Cambridge University Press:  26 February 2010

D. A. Brannan
D. A. Brannan
Affiliation:
Imperial College, University of London.
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Extract

Let be the class of normalised polynomials of the form:

of degree n which are univalent in |z| < 1, and let be the class of “polynomials” of the form

of degree n which are univalent in 0 < |z| < 1. In this note we discuss the coefficients of polynomials in (k = 2, 3, 4) and (k = 2, 3).

Type
Research Article
Information
Mathematika , Volume 14 , Issue 2 , December 1967 , pp. 165 - 169
Copyright
Copyright © University College London 1967

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References

1.Cowling, V. F. and Royster, W. C.. To appear.Google Scholar
2.Dieudonné, J., “Sur le rayon d'univalence des polynomes”, C. R. Acad. Sci Paris, 192 (1931), 78–81.Google Scholar
3.Marden, M., The geometry of the zeros of a polynomial in a complex variable (New York, 1949).Google Scholar