Faber Polynomial Coefficients and Applications in Analytic Function Class

Through this paper, by using the subordination definition, the ℘-analogues Cătaş operator I℘nλ,I, complex order, and biunivalent functions with coefficients introduced by Faber polynomial expansion, we introduced the new class S℘,n∗f,λ,I,ξ,α,ϕ. A Faber polynomial is known as a sequence of polynomials that are used to approximate an analytic function on a compact set. This new class provides a framework for exploring various properties of biunivalent functions. We obtained new subclasses from the class S℘,n∗f,λ,I,ξ,α,ϕ. In addition, we generalized and improved many previous classes. We obtained estimates for the bounds of the coefficients for functions belonging to the class S℘,n∗f,λ,I,ξ,α,ϕ. We estimate the initial coefficients of the functions from the indicated class and determine S℘,n∗f,λ,I,ξ,α,ϕ. In addition, since Faber polynomials are closely related to approximation and filtering, the results may also be applied in areas such as signal recovery and problems involving Gaussian weights.