Initial Coefficient Behavior of Bi-Univalent Functions Defined Through Bernoulli Polynomial Subordination

The study of coefficient problems for bi-univalent functions continues to play a central role in geometric function theory due to its analytical depth and wide range of applications. In this paper, we introduce a new subclass of bi-univalent functions defined through subordination to the generating function of Bernoulli polynomials. We derive explicit upper bounds for the initial Taylor–Maclaurin coefficients and establish a corresponding Fekete–Szegö-type inequality for functions in this class. The results obtained provide refined estimates that extend several known findings in the literature and reveal the effectiveness of Bernoulli polynomial subordination as a unifying framework for investigating coefficient problems in the theory of bi-univalent functions. Various special cases are also discussed to demonstrate the scope and applicability of the main results.