Second Hankel Determinant for a Bi-univalent Function Subclass Based Gegenbauer (Ultraspherical) Polynomials
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i2.5968Keywords:
Gegenbauer Polynomial, , , Analytic and Bi-univalent Functions,, Hankel Determinant,Abstract
In this paper, we aim to establish a new upper bound approximation for the second Hankel determinant utilizing a certain subclass of the class of normalized analytic and bi-univalent functions in the open unit disk \,$\mathbb{U}$\,. These functions have inverses with a bi-univalent analytic continuation to \,$\mathbb{U}$\, and are associated with orthogonal polynomials; namely, Gegenbauer polynomials that satisfy subordination conditions on \,$\mathbb{U}$. Finally, we introduce new essential results derived by specializing the parameter \,$\tau$\, employed in our foundational finding.
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Copyright (c) 2025 Abdelbaset Zeyani, Abdulmtalb Hussen
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