In the present investigation, with motivation from the pioneering work of Srivastava et al. [28], which in recent years actually revived the study of analytic and bi-univalent functions, we introduce the subclasses T * Σ (n, β) and T Σ (n, α) of analytic and bi-univalent function class Σ defined in the open unit disk U = {z ∈ C : |z| < 1} and involving the Sălăgean derivative operator D n. 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