Gegenbauer Polynomials For a New Subclass of Bi-univalent Functions
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In this study, we introduce and investigate a novel subclass of analytic biunivalent functions, which we define using Gegenbauer polynomials. We derive the initial coefficient bounds for |a2|, |a3|, and |a4|, and establish Fekete-Szego inequalities for this class. In addition, we confirm that Brannan and Clunie’s conjecture, |a2| ≤ √2, is valid for this subclass. To facilitate better understanding, we provide visualizations of the functions, using appropriately chosen parameters.
Abstract
In this study, we introduce and investigate a novel subclass of analytic biunivalent functions, which we define using Gegenbauer polynomials. We derive the initial coefficient bounds for |a2|, |a3|, and |a4|, and establish Fekete-Szego inequalities for this class. In addition, we confirm that Brannan and Clunie’s conjecture, |a2| ≤ √2, is valid for this subclass. To facilitate better understanding, we provide visualizations of the functions, using appropriately chosen parameters.
참고문헌 (7)
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