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

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 | $|a_{m+1}|$ and | a 2 m + 1 | $|a_{2m+1}|$ , 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 ) $MF-S_{\Sigma ,m}^{p,q}(h)$ , M F − S Σ , m p , q ( s ) $MF-S_{\Sigma , m}^{p,q}(s)$ , and M F − S Σ , m b , d $MF-S_{\Sigma , m}^{b,d}$ . Quantum calculus aspects are also considered in this study to enhance its novelty and to obtain more interesting results.

Keywords

• Analytic functions
• Bi-univalent functions
• Fekete–Szegö functional
• m-fold symmetric
• Coefficient estimates
• Coefficient bounds