Subfamilies of bi-univalent functions governed by Bernoulli polynomials

In the context of univalent function theory, special functions play an important role and have been studied by a number of researchers earlier. This article presents and examines two subfamilies of bi-univalent functions that are governed by Bernoulli polynomials in the open unit disk. We obtain limits on initial coefficients for functions in the specified subfamilies. The Fekete-Szegő problem is also addressed for the elements of the subfamilies that have been defined. We also present some new results and discuss pertinent links to earlier findings.