In the current article, we introduce several new subclasses of m-fold symmetric analytic and bi-univalent functions associated with bounded boundary and bounded radius rotation within the open unit disk D. Utilizing the Faber polynomial expansion, we derive upper bounds for the coefficients |bmk+1| and establish initial coefficient bounds for |bm+1| and |b2m+1|. Additionally, we explore the Fekete–Szegö inequalities applicable to the functions that fall within these newly defined subclasses.
