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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Distortion properties of $p$-fold symmetric alpha-starlike functions
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by H. B. Coonce and S. S. Miller PDF
Proc. Amer. Math. Soc. 44 (1974), 336-340 Request permission

Abstract:

Starlike functions $f$ which are of Mocanu type $\alpha$ and have power series of the form \[ f(z) = z + {a_{p + 1}}{z^{p + 1}} + {a_{2p + 1}}{z^{2p + 1}} + \cdots ,\] where $p = 1,2,3, \cdots$, are shown to satisfy the relation $f(z) = {[g({z^p})]^{1/p}}$ where $g$ is of Mocanu type $p\alpha$ with power series $g(z) = z + {b_2}{z^2} + {b_3}{z^3} + \cdots$. Distortion results dealing with the $\tfrac {1}{4}$-theorem and bounds on $|f(z)|$ are obtained.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 44 (1974), 336-340
  • MSC: Primary 30A32
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0344440-2
  • MathSciNet review: 0344440