In this article, we derive some estimates for the Taylor-Maclaurin coefficients of functions that belong to a new general subclass $ \Upsilon_\Sigma(\delta, \rho, \tau, n;\varphi) $ of bi-univalent functions in an open unit disk, which is defined by using the Ruscheweyh derivative operator and the principle of differential subordination between holomorphic functions. Our results are more accurate than the previous works and they generalize and improve some outcomes that have been obtained by other researchers. Under certain conditions, the derived bounds are smaller than those in the previous findings. Furthermore, if we specialize the parameters, several repercussions of this generic subclass will be properly obtained.
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