On the coefficient estimates for a subclass of m-fold symmetric bi-univalent functions

In this work, we introduce and investigate a subclass \(\mathcal{G}_{\Sigma_m}^{h,p}(\lambda,\gamma)\) of analytic and bi-univalent functions when both \(f\) and \(f^{-1}\) are m-fold symmetric in the open unit disk \(\mathbb{U}\). Moreover, we find upper bounds for the initial coefficients \(|a_{m+1}|\) and \(|a_{2m+1}|\) for functions belonging to this subclass \(\mathcal{G}_{\Sigma_m}^{h,p}(\lambda,\gamma)\). The results presented in this paper would generalize and improve those that were given in several recent works.