Coefficient Bounds for a New Subclass of Bi-Univalent Functions Involving the Salagean Deferential Operator

The study of bi-univalent functions has attracted considerable attention in Geometric Function Theory due to its importance in coefficient problems and related applications. Motivated by recent developments involving differential operators, this paper introduces two new subclasses of bi-univalent functions belonging to the family Σ in the open unit disk by means of the S˘al˘agean differential operator. For these subclasses, sharp estimates for the coefficients |b2| and |b3| are obtained. The results presented in this work extend and generalize several earlier findings in the literature. Moreover, the proposed framework provides a useful basis for further investigations, including higher-order coefficient bounds, Fekete-Szego inequalities, Hankel determinants, and other related problems associated with these subclasses.