Upper Bounds and Fekete–Szegö Problem for Bi-Univalent Functions Involving Bazilevič and λ-Pseudo Functions Related to Lucas-Balancing Polynomials

This work introduces two novel classes of bi-univalent functions, denoted by ℬΣ(μ,γ,λ;r) and ΡΣ(μ,γ,λ;r), linked to Lucas-Balancing polynomials within the open unit disk. For functions pertaining to these newly defined classes, we establish estimates for the early Taylor–Maclaurin coefficients |a2| and |a3|. Furthermore, the Fekete–Szegö functional inequalities are evaluated for these families. Subsequently, relevant particular cases and corollaries stemming from our primary findings are emphasized through parameter specialization.