Faber Polynomial Coefficients and Applications in Analytic Function Class

Samar Mohamed and Fatma Z. El-Emam

Journal of Mathematics, 2025, vol. 2025, 1-16

Abstract: 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.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6797149

DOI: 10.1155/jom/6797149

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