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

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 $|a_3|$.

Keywords

• analytic function
• starlike function
• convex function
• bi-univalent function
• bounded boundary rotation