  Inspired by the recent works of Srivastava et al. (2010), Frasin and Aouf
(2011), and Caglar et al. (2013), we introduce and investigate in the present
paper two new general subclasses of the class consisting of normalized analytic
and bi-univalent functions in the open unit disk U. For functions belonging to
these general subclasses introduced here, we obtain estimates on the
Taylor-Maclaurin coefficients |a_2| and |a_3|. Several connections to some of
the earlier known results are also pointed out. The results presented in this
paper would generalize and improve those in related works of several earlier
authors.
