Coefficient estimates for certain class of bi-Bazilevič bounded functions with complex of order

Abstract In this paper, we introduce a new class of Bazilevič bi-univalent functions with complex order, defined in the open unit disk by employing bounded analytic functions. We establish precise bounds for the second and third Taylor–Maclaurin coefficients of functions in this class. Our results generalize several known coefficient estimates in geometric function theory. Furthermore, we examine important special cases that demonstrate the practical implications of our findings.