Fekete–Szeg˝o Inequalities for New Subclasses of Bi-Univalent Functions Defined by S˘al˘agean q-Differential Operator

In this paper, we introduce a new operator based on the S\u{a}l\u{a}gean \( q \)-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--Szeg\H{o} inequalities for the function classes \( \mathcal{M}_{\sigma,q,\Sigma}^{\zeta,m}(\leftthreetimes, \kappa, \alpha) \) and \( \mathcal{M}_{\sigma,q,\Sigma}^{\zeta,m}(\gamma,\leftthreetimes, \kappa) \). Through our analysis, we derive several important results, including some special cases that we present in this paper as Corollaries.