Faber Polynomial Coefficients and Applications in Analytic Function Class

Through this paper, by using the subordination definition, the ℘ ‐analogues Cătaş operator , complex order, and biunivalent functions with coefficients introduced by Faber polynomial expansion, we introduced the new class . 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 . In addition, we generalized and improved many previous classes. We obtained estimates for the bounds of the coefficients for functions belonging to the class We estimate the initial coefficients of the functions from the indicated class and determine 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.