The derivative of Bazilevič functions

London, R. R.; Thomas, D. K.

doi:10.1090/S0002-9939-1988-0958074-X

The derivative of Bazilevič functions
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by R. R. London and D. K. Thomas

Proc. Amer. Math. Soc. 104 (1988), 235-238

DOI: https://doi.org/10.1090/S0002-9939-1988-0958074-X

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Corrigendum: Proc. Amer. Math. Soc. 109 (1990), 1143.

Abstract:

For $\alpha {\text { > }}0$, let ${B_1}(\alpha )$ be the class of normalised analytic functions $f$ defined in the open unit disc $D$ such that ${\text {Re(}}f(z)/z{{\text {)}}^{\alpha - 1}}f’(z){\text { > }}0$ for $z \in D$. Sharp upper and lower bounds are obtained for $\left | {zf’(z)/f(z)} \right |$ when $f \in {B_1}(\alpha )$.

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On the derivative of some Bazilevič functions

An estimate for functions with positive real part

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