In this investigations, we generalize the multiplier operator analytic and univalent functions in the form f(z)=z+∑_{k=2}^{∞}a_{k}z^{k} defined in the open unit disc U={z:z∈ℂ and |z|<1}. This new operator contains many other operators which were defined by many authors such as Cho and kim [8], Cho and Srivastava [9], Cătaş et al. [7], Uralegaddi and Samanatha [13], Aouf et al. [4, with w=0] and others for different values of its parameters. Using the principle of subordination and this new operator, we define two subclasses of starlike and convex functions S_{n}^{∗}(λ,s,A,B,α) and C_{n}^{∗}(λ,s,A,B,α) respectively, which in turn generalize many other classes for the special values of the parameters. Using the definition and the lemma of Wilf [14], we obtain many results of subordinating factor sequence for these classes which lead to obtaining that also for the special subclasses by using the technique of Attiya [5], Frasin [10] and recently by Aouf and Mostafa [2,3].