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Proceedings of the American Mathematical Society
Article . 1978 . Peer-reviewed
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Proceedings of the American Mathematical Society
Article . 1978 . Peer-reviewed
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Goodman’s conjecture and the coefficients of univalent functions

Goodman's conjecture and the coefficients of univalent functions
Authors: Lyzzaik, Abdallah; Styer, David;

Goodman’s conjecture and the coefficients of univalent functions

Abstract

Goodman’s conjecture (for a bound on the modulus of the nth coefficient of a p-valent function as a linear combination of the moduli of the first p coefficients) is considered in the special case of functions which are polynomials of univalent functions. For such functions, it is shown that Goodman’s conjecture is equivalent to a set of coefficient conjectures for normalized univalent functions.

Keywords

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.), Coefficient problems for univalent and multivalent functions of one complex variable

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
bronze