The study of coefficient estimates and Fekete–Szegö inequalities for the new classes of m-fold symmetric bi-univalent functions defined using an operator.

The objective of this paper is to introduce new classes of m-fold symmetric bi-univalent functions. We discuss estimates on the Taylor–Maclaurin coefficients | a m + 1 | and | a 2 m + 1 | , and the Fekete–Szegő problem is also considered for the new classes of functions introduced. We denote these classes by M F − S Σ , m p , q (h) , M F − S Σ , m p , q (s) , and M F − S Σ , m b , d . Quantum calculus aspects are also considered in this study to enhance its novelty and to obtain more interesting results. [ABSTRACT FROM AUTHOR]