Coefficient Estimates and Symmetry Analysis for Certain Families of Bi-Univalent Functions Defined by the 𝒒-Bernoulli Polynomial

In the present work, we define certain families, MΣμ,Υ,ℷ,q; x and NΣμ,Υ,ℷ,q; x, of normalized holomorphic and bi-univalent functions associated with Bazilevič functions and ℷ-pseudo functions involving the q-Bernoulli polynomial, which is defined by the symmetric nature of quantum calculus in the open unit disk U. We determine the upper bounds for the initial symmetry Taylor–Maclaurin coefficients and the Fekete–Szegö-type inequalities of functions in the families we have introduced here. In addition, we indicate certain special cases and consequences for our results.