In this current study, we aim to give some results for third-order differential subordination and superordination for analytic functions in involving the generalized operator . The results are derived by investigating relevant classes of admissible functions. Some new results on differential subordination and superordination with some sandwich theorems are obtained. Moreover, several particular cases are also noted. The properties and results of the differential subordination are symmetry to the properties of the differential superordination to form the sandwich theorems.

In the present paper, we introduce two new subclasses of  the class consisting of analytic and bi-univalent functions in the open unit disk . Also, we obtain the estimates on the Taylor-Maclurin   coefficients and for functions in these subclasses. We obtain new special cases for our results.

By using of linear  operator, we obtain some Subordinations  and superordinations results for certain normalized meromorphic univalent analytic functions in the in the punctured open unit disk   Also we derive some sandwich theorems .