Sharp coefficient inequalities for certain subclasses of bi-univalent Bazilevi\v{c} functions
Commun. Korean Math. Soc. 2022 Vol. 37, No. 1, 113-123
Published online November 4, 2021
Printed January 31, 2022
Amol Bhausaheb Patil
AISSMS College of Engineering
Abstract : In the present paper, we introduce the subclasses $\mathfrak{B}_{1\Sigma}(\mu)$, $\mathrm{B}_{1\Sigma}(\mu,\gamma)$ and $\mathit{U}_{\Sigma}(\mu,\gamma)$ of bi-univalent Bazilevi\v{c} functions which are defined in the open unit disk $\mathbb{D}$. Further, we obtain sharp estimates on initial coefficients $a_2$, $a_3$, $a_4$ and also sharp estimate on the Fekete-Szeg\"{o} functional $a_3-k{a}_{2}^{2}$ for the functions belong to these subclasses.
Keywords : Analytic function, univalent function, bi-univalent function, star-like function, Bazilevi\v{c} function
MSC numbers : Primary 30C45, 30C50
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