Mohamed Illafe
School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Penang, Malaysia. & School of Mathematics Engineering and Technology, Navajo Technical University, Lowerpoint Rd State Hwy 371 Crownpoint NM, 87313, USA.

Maisarah Haji Mohd
School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Penang, Malaysia.

Feras Yousef
Department of Mathematics, The University of Jordan, 11942, Amman, Jordan. & Jadara University Research Center, Jadara University, 21110, Irbid, Jordan.

Shamani Supramaniam
School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Penang, Malaysia.

DOI https://doi.org/10.33889/IJMEMS.2024.9.5.065

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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.

Keywords- Hankel determinant, Gegenhauer polynomials, Bi-univalent function, Fekete-Szegö functional.

Citation

Illafe, M., Mohd, M. H. Yousef, F., & Supramaniam, S. (2024). Bounds for the Second Hankel Determinant of a General Subclass of Bi-Univalent Functions. International Journal of Mathematical, Engineering and Management Sciences, 9(5), 1226-1239. https://doi.org/10.33889/IJMEMS.2024.9.5.065.