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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the coefficients of $p$-valent functions which are polynomials of univalent functions
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by Pavel G. Todorov PDF
Proc. Amer. Math. Soc. 97 (1986), 605-608 Request permission

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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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 97 (1986), 605-608
  • MSC: Primary 30C50; Secondary 30C30
  • DOI: https://doi.org/10.1090/S0002-9939-1986-0845973-0
  • MathSciNet review: 845973