Fekete–Szeg˝o Inequalities for New Subclasses of Bi-Univalent Functions Defined by S˘al˘agean q-Differential Operator (European Journal of Pure and Applied Mathematics, 2025)
In this paper, we introduce a new operator based on the Sălăgean \( q \)-differential approach to define a new class of analytic functions. Using this operator, we obtain estimates for the first two coefficients in the Taylor series, \( |a_2| \) and \( |a_3| \). A significant part of the study focuses on the Fekete--Szegő inequalities for the function classes \( \mathcal{M}_{σ,q,Σ}^{ζ,m}(\leftthreetimes, κ, α) \) and \( \mathcal{M}_{σ,q,Σ}^{ζ,m}(γ,\leftthreetimes, κ) \). Through our analysis, we derive several important results, including some special cases that we present in this paper as Corollaries.
Keywords: Analytic Functions, $q$-Sălăgean Operator, Starlike Functions, Taylor Coefficients