We present several new results for fourth-order differential subordination and superordination in this paper by using the differential linear operator . Relevant connections between the new results presented here and those considered in previous works are addressed. The properties and results concerning the differential subordination theory are symmetric to the properties obtained using the differential superordination theory, and by combining them, sandwich-type theorems are obtained.

In this research paper, we explain the use of  the convexity and the starlikness properties of  a given function  to generate  special properties of differential subordination and superordination functions in the classes of analytic functions that have  the form   in the unit disk. We also show the significant of  these properties to derive sandwich results when the Srivastava- Attiya operator   is used.

In this paper we will work with the decomposition character table for symmetric groupsS 4 to character table of all subgroups by using a new young subgroup of typeS 2 × S 2 .