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    Coefficient estimation utilizing the faber polynomial for a subfamily of bi-univalent functions
    (MDPI, 2023) Alsoboh, Abdullah; Amourah, Ala; Sakar, Fethiye Müge; Ogilat, Osama; Gharib, Gharib Mousa; Zomot, Nasser
    The paper introduces a new family of analytic bi-univalent functions that are injective and possess analytic inverses, by employing a q-analogue of the derivative operator. Moreover, the article establishes the upper bounds of the Taylor–Maclaurin coefficients of these functions, which can aid in approximating the accuracy of approximations using a finite number of terms. The upper bounds are obtained by approximating analytic functions using Faber polynomial expansions. These bounds apply to both the initial few coefficients and all coefficients in the series, making them general and early, respectively.
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    Öğe
    Exploration of New Classes of Bi-univalent Functions Defined by the Subordination Principle Using q-Gegenbauer Polynomials
    (Springer, 2024) Alsoboh, Abdullah; Amourah, Ala; Alatawi, Maryam Salem; Gharib, Gharib; Sakar, Fethiye
    In 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.