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

Yumao Li; K. Vijaya; G. Murugusundaramoorthy; Huo Tang; Yumao Li; K. Vijaya; G. Murugusundaramoorthy; Huo Tang

doi:10.3934/math.2020215

AIMS Mathematics

2020, Volume 5, Issue 4: 3346-3356. doi: 10.3934/math.2020215

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Research article

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

Received: 14 February 2020 Accepted: 17 March 2020 Published: 30 March 2020
MSC : 30C45, 30C50

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 $|a_3|$.
- 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[J]. AIMS Mathematics, 2020, 5(4): 3346-3356. doi: 10.3934/math.2020215

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Abstract

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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