On coefficient inequalities of certain subclasses of bi-univalent functions involving the Salagean operator

Abstract

In the present investigation, by involving the Salagean differential operator $D^{n}$, we introduce the subclasses $\mathcal{T}_{\Sigma}^{*}(n, \beta)$ and $\mathcal{T}_{\Sigma}(n, \alpha)$ of bi-univalent function class $\Sigma$ defined in the open unit disk $\mathbb{U}=\left\lbrace z\in \mathbb{C} : |z|<1 \right\rbrace$. Moreover, we derive estimates on the initial coefficients $|a_2|$ and $|a_3|$ for functions in these subclasses and pointed out connections with some earlier known results.