Faber polynomial coefficient estimates for analytic bi-univalent functions associated with Gregory coefficients
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Abstract
In this work, we consider the function
\begin{equation*}
\Psi (z)=\frac{z}{\ln \left( 1+z\right) }=1+\sum_{n=1}^{\infty }G_{n}z^{n}
\end{equation*}
whose coefficients $G_{n}$ are the Gregory coefficients related to Stirling numbers of the first kind and introduce a new subclass $\mathcal{G}_{\Sigma }^{\lambda,\mu}\left( \Psi \right) $ of analytic bi-univalent functions subordinate to the function $\Psi $.
For functions belong to this class, we investigate the estimates for the general Taylor-Maclaurin coefficients by using the Faber polynomial expansions. In certain cases, our estimates improve some of those existing coefficient bounds.
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