Texture analysis using Horadam polynomial coefficient estimate for the class of Sakaguchi kind function.

Area of Science:

• Complex Analysis
• Geometric Function Theory

Background:

• Bi-univalent functions are a significant subclass of analytic functions, characterized by the property that both the function and its inverse are univalent.
• Understanding coefficient bounds is crucial for characterizing the geometric properties and behavior of these functions within the open unit disk.
• Horadam polynomials offer a versatile framework for defining and analyzing families of analytic functions.

Purpose of the Study:

• To determine the initial coefficient bounds for a newly introduced bi-univalent function class.
• To investigate the application of Horadam polynomials and their generating functions in estimating these bounds.
• To explore the Fekete-Szegö inequalities for the defined function class.

Main Methods:

• Utilizing the properties of Horadam polynomials and their generating functions.
• Applying established techniques in geometric function theory to derive coefficient bounds.
• Calculating Fekete-Szegö inequalities for the bi-univalent functions under consideration.

Main Results:

• The initial coefficient bounds for the bi-univalent function class [Formula: see text] were successfully derived.
• Estimates for [Formula: see text] and [Formula: see text] were obtained using Horadam polynomials.
• Fekete-Szegö inequalities were computed for the functions within the defined class.

Conclusions:

• The research provides novel coefficient bounds for a specific class of bi-univalent functions.
• The study demonstrates the utility of Horadam polynomials in analytic number theory and function theory.
• An application of Horadam polynomials in computer vision is presented, highlighting interdisciplinary relevance.