Coefficient Estimates and the Fekete-Szego Problem for New Classes of m-Fold Symmetric Bi-Univalent Functions

The results presented in this paper deal with the classical but still prevalent problem of introducing new classes of m-fold symmetric bi-univalent functions and studying properties related to coefficient estimates. Quantum calculus aspects are also considered in this study in order to enhance its novelty and to obtain more interesting results. We present three new classes of bi-univalent functions, generalizing certain previously studied classes. The relation between the known results and the new ones presented here is highlighted. Estimates on the Taylor-Maclaurin coefficients |a(m+1)| and |a(2m+1)| are obtained and, furthermore, the much investigated aspect of Fekete-Szego functional is also considered for each of the new classes.