Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Gegenbauer Polynomials For a New Subclass of Bi-univalent Functions

  • Received : 2023.12.02
  • Accepted : 2024.06.12
  • Published : 2024.09.30
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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.

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References

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