Sub classes of Bi-Univalent Functions Defined by Salagean type $q-$ Difference Operator

In this paper, we introduce and investigate a new subclass of the function class $\mathrm{\Sigma }$ of bi-univalent functions defined in the open unit disk, which are associated with the S\u{a}l\u{a}gean type $q-$ difference operator and satisfy some subordination conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients $\mathrm{\mid }{a}_2\mathrm{\mid }$ and $\mathrm{\mid }{a}_3\mathrm{\mid }$ for functions in the new subclass introduced here. Several (known or new) consequences of the results are also pointed out. Further we obtain Fekete-Szeg$\ddot{o}$ inequality for the new function class.