Some remarks for subclasses of bi-univalent functions defined by Ruscheweyh derivative operator

This paper presents two subclasses of analytic and bi-univalent functions associated with the Ruscheweyh derivative operator to investigate the bounds for |a2| and |a3|, where a2 and a3 are the initial Tayler-Maclaurin coefficients. The current results would generalize and improve some corresponding recent works. Additionally, in certain cases, our estimates correct some of the existing coefficient bounds.