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

Abstract

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_{2m+1}|, and the Fekete–Szegő problem is also considered for the new classes of functions introduced. We denote these classes by MF-S_{Sigma ,m}^{p,q}(h), MF-S_{Sigma , m}^{p,q}(s), and MF-S_{Sigma , m}^{b,d}. Quantum calculus aspects are also considered in this study to enhance its novelty and to obtain more interesting results.