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Behavior of Coefficients of Inverses of α-Spiral Functions

Published online by Cambridge University Press:  20 November 2018

Richard J. Libera  and
Eligiusz J. Złotkiewicz
Richard J. Libera
Affiliation:
University of Delaware, Newark, Delaware
Eligiusz J. Złotkiewicz
Affiliation:
Uniwersytet Marii Curie-Sklodowskiej, Lublin, Polska
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If f(z) is univalent (regular and one-to-one) in the open unit disk Δ, Δ = {z ∊ C:│z│ < 1}, and has a Maclaurin series expansion of the form

(1.1)

then, as de Branges has shown, │ak│ = k, for k = 2, 3, … and the Koebe function.

(1.1)

serves to show that these bounds are the best ones possible (see [3]). The functions defined above are generally said to constitute the class .

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 6 , 01 December 1986 , pp. 1329 - 1337
Copyright
Copyright © Canadian Mathematical Society 1986

References

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