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The motivation of the present article is to define the (p−q)-Wanas operator in geometric function theory by the symmetric nature of quantum calculus. We also initiate and explore certain new families of holormorphic and bi-univalent functions AE(λ,σ,δ,s,t,p,q;ϑ) and SE(μ,γ,σ,δ,s,t,p,q;ϑ) which are defined in the unit disk U associated with the (p−q)-Wanas operator. The upper bounds for the initial Taylor–Maclaurin coefficients and Fekete–Szegö-type inequalities for the functions in these families are obtained. Furthermore, several consequences of our results are pointed out based on the various special choices of the involved parameters.

Initial Coefficient Estimates and Fekete–Szegö Inequalities for New Families of Bi-Univalent Functions Governed by (p − q)-Wanas Operator