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
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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