Alsoboh, AbdullahAmourah, AlaAlatawi, Maryam SalemGharib, GharibSakar, Fethiye2025-02-222025-02-222024978-981974875-42194-1009https://doi.org/10.1007/978-981-97-4876-1_24https://hdl.handle.net/11468/298538th International Arab Conference on Mathematics and Computations, IACMC 2023 -- 10 May 2023 through 12 May 2023 -- Zarqa --321039In this study, we introduce a new class of bi-univalent functions constructed using q-Gegenbauer polynomials. We analyze and characterize this newly defined class of functions, and derive estimates for the Taylor-Maclaurin coefficients |a2| and |a3|. Additionally, we investigate the formulation of functional problems specific to functions within this subclass, namely a3-σa22 (commonly known as the Fekete-Szegö problem). By systematically exploring parameter specialization, we discover a range of novel outcomes that shed light on various aspects of our main results, contributing to a broader understanding of the mathematical landscape under investigation. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.eninfo:eu-repo/semantics/closedAccessAnalytic functionsFekete-Szegö functionalq-calculusq-Gegenbauer polynomialsTaylor expansionThe subordination principalUnivalent and bi-univalent functionsConference Object4663433552-s2.0-8520691258610.1007/978-981-97-4876-1_24Q4