Coefficient estimates for certain class of bi-univalent functions associated with κ-Fibonacci numbers

Abstract

In the present work, we propose to introduce and investigate a new class SL_Σ^q,μ (γ, λ, n, p_κ) of the function class Σ of bi-univalent functions related to κ-Fibonacci numbers defined in the open unit disk, which is associated with the Salagean type q-difference operator and satisfy some subordination conditions. We obtain coefficient bounds for the Taylor–Maclaurin coefficients |a₂| and |a₃| of the functions in the new class. Furthermore, we solve the Fekete–Szegö functional for functions in the class SL_Σ^q,μ (γ, λ, n, p_κ).