AIMS Mathematics, 2020, 5(4): 3346-3356. doi: 10.3934/math.2020215.

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On new subclasses of bi-starlike functions with bounded boundary rotation

1 School of Mathematics and Computer Sciences, Chifeng University, Chifeng 024000, People’s Republic of China
2 Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Deemed to be University, Vellore-632014, India

In this paper, we introduce two new classes $\mathcal{B}_{\Sigma}^\lambda(m,\mu)$ of $\lambda$-pseudo bi-starlike functions and $\mathcal{L}_{\Sigma}^\eta(m,\beta)$ to determine the bounds for $|a_2|$ and $|a_3|,$ where $a_2$, $a_3$ are the initial Taylor coefficients of $f\in\mathcal{B}_{\Sigma}^\lambda(m,\mu)$ and $f\in\mathcal{L}_{\Sigma}^\eta(m,\beta).$ Also, we attain the upper bounds of the Fekete-Szegö inequality by means of the results of $|a_2|$ and $|a_3|$.
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Keywords analytic function; starlike function; convex function; bi-univalent function; bounded boundary rotation

Citation: Yumao Li, K. Vijaya, G. Murugusundaramoorthy, Huo Tang. On new subclasses of bi-starlike functions with bounded boundary rotation. AIMS Mathematics, 2020, 5(4): 3346-3356. doi: 10.3934/math.2020215

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