International Journal of Mathematical, Engineering and Management Sciences (Oct 2024)
Bounds for the Second Hankel Determinant of a General Subclass of Bi-Univalent Functions
Abstract
The Hankel determinant, which plays a significant role in the theory of univalent functions, is investigated here in the context of bi-univalent analytic functions. Specifically, this paper is dedicated to deriving an upper-bound estimate for the second-order Hankel determinant for a general subclass of bi-univalent analytic functions that incorporate Gegenbauer polynomials within the unit disk. Through the careful specialization of parameters in our main result, we unveil several novel findings.
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