We introduce and examine two new subclass of bi-univalent function Σ, defined in the open unit disk, based on Sălăgean-type q-difference operators which are subordinate to the involution numbers. We find initial estimates of the Taylor–Maclaurin coefficients |a2| and |a3| for functions in the new subclass introduced here. We also obtain a Fekete–Szegö inequality for the new function class. Several new consequences of our results are pointed out, which are new and not yet discussed in association with involution numbers.
