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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 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Functions with real part greater than $\alpha$
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by Carl P. McCarty
Proc. Amer. Math. Soc. 35 (1972), 211-216
DOI: https://doi.org/10.1090/S0002-9939-1972-0298014-0

Abstract:

Let ${\mathcal {P}_b}(\alpha )$ denote the class of functions $P(z) = 1 + b(1 - \alpha )z + \cdots$ which are analytic and satisfy $\operatorname {Re} \{ P(z)\} > \alpha$ for $|z| < 1$ where $\alpha \in [0,1)$ and $b \in [0,2]$. We demonstrate some inequalities involving $|Pā€™(z)|$ and $|Pā€™(z)/P(z)|$ dependent on b and $\alpha$ which are subsequently applied to the class of functions whose derivative lies in ${\mathcal {P}_b}(\alpha )$ to obtain distortion, covering, and radius of convexity properties.
References
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Bibliographic Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 35 (1972), 211-216
  • MSC: Primary 30A76
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0298014-0
  • MathSciNet review: 0298014