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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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Generating functions for some classes of univalent functions
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by Zdzisław Lewandowski, Sanford Miller and Eligiusz Złotkiewicz PDF
Proc. Amer. Math. Soc. 56 (1976), 111-117 Request permission

Abstract:

Let $P(z) = {e^{i\beta }} + {p_1}z + {p_2}{z^2} + \cdots$ be regular in the unit disc $\Delta$ with $|\beta | < \pi /2$, and let $\psi (u,v)$ be a continuous function defined in a domain of ${\mathbf {C}} \times {\mathbf {C}}$. With some very simple restrictions on $\psi (u,v)$ the authors prove a lemma that $\operatorname {Re} \psi (p(z),zp’(z)) > 0$ implies $\operatorname {Re} p(z) > 0$. This result is then used to generate subclasses of starlike, spirallike and close-to-convex functions.
References
Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 56 (1976), 111-117
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0399438-7
  • MathSciNet review: 0399438