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

AbstractThe objective of this paper is to introduce new classes of m-fold symmetric bi-univalent functions. We discuss estimates on the Taylor–Maclaurin coefficients$|a_{m+1}|$|am+1|and$|a_{2m+1}|$|a2m+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−SΣ,mp,q(h),$MF-S_{\Sigma , m}^{p,q}(s)$MF−SΣ,mp,q(s), and$MF-S_{\Sigma , m}^{b,d}$MF−SΣ,mb,d. Quantum calculus aspects are also considered in this study to enhance its novelty and to obtain more interesting results.