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 $|a_3|$.

Topics & Concepts