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Faber polynomial coefficient estimates for analytic bi-univalent functions associated with Gregory coefficients

Serap Bulut
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2024.06|한국수학논문집 (Korean Journal of Mathematics)|제32권 제2호|pp. 285-295

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키워드

Analytic functioncoefficient estimatesbi-univalent functionFaber polynomialsGregory coefficients
주제분류수학

초록

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.

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.

참고문헌 (34)

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