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*?(n,?)
and T?(n,?) of analytic and bi-univalent function class ? defined in the
open unit disk U = {z ? C : |z| < 1g and involving the S?l?gean derivative
operator Dn. Moreover, we derive estimates on the initial coefficients |a2|
and |a3| for functions in these subclasses and pointed out connections with
some earlier known results.