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Gegenbauer Polynomials For a New Subclass of Bi-univalent Functions

Publication Type : Journal Article

Source : Kyungpook Mathematical Journal

Url : https://koreascience.or.kr/article/JAKO202431243264267.page

Campus : Chennai

School : School of Engineering

Year : 2024

Abstract : In this study, we introduce and investigate a novel subclass of analytic bi-univalent functions, which we define using Gegenbauer polynomials. We derive the initial coefficient bounds for |a2|, |a3|, and |a4|, and establish Fekete-Szegö inequalities for this class. In addition, we confirm that Brannan and Clunie's conjecture, ${\mid}a_2{\mid}\,{\leq}\,{\sqrt{2}}$, is valid for this subclass. To facilitate better understanding, we provide visualizations of the functions, using appropriately chosen parameters.

Cite this Research Publication : Saravanan G, Baskaran S, Vanithakumari B, Wanas A.K, Gegenbauer Polynomials For a New Subclass of Bi-univalent Functions, Kyungpook Mathematical Journal, 2024

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