The study of coefficient estimates and Fekete-Szego 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(2m+1)|, and the Fekete-Szego 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.

Automated summary

This paper introduces new classes of m-fold symmetric bi-univalent functions and discusses estimates on the Taylor-Maclaurin coefficients |a(m+1)| and |a(2m+1)|. The Fekete-Szego problem for the new classes of functions is also considered. The study incorporates aspects of quantum calculus to enhance novelty and obtain more interesting results.