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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the coefficients of $ p$-valent functions which are polynomials of univalent functions


Author: Pavel G. Todorov
Journal: Proc. Amer. Math. Soc. 97 (1986), 605-608
MSC: Primary 30C50; Secondary 30C30
MathSciNet review: 845973
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Abstract: We give explicit representations of the coefficients of $ p$-valent functions which are polynomials of univalent functions of the class $ S$. With their help we prove the Goodman conjecture in the special case that $ f(z) = {[\varphi (z)]^p}$, $ \varphi (z)$ in $ S$. We also obtain sharp upper bounds for the coefficients of the considered $ p$-valent functions in terms of the coefficients of the two component functions.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0845973-0
Keywords: $ p$-valent functions, univalent functions, the Goodman conjecture
Article copyright: © Copyright 1986 American Mathematical Society