Coefficient Estimates for Some Subclasses of m–Fold Symmetric Bi-Univalent Functions

Abstract

The articles introduces and investigates two new subclasses of the bi-univalent functions These are analytical functions related to the m-fold symmetric function We calculate the initial coefficients for all the functions that belong to them, as well as the coefficients for the functions that belong to a field where finding these coefficients requires a complicated method. Between the remaining results, the upper bounds for the initial coefficients are found in our study as well as several examples. We also provide a general formula for the function and its inverse in the m-field. A function is called analytical if it does not take the same values twice It is called a univalent function if it is analytical at all its points, and the function is called a bi-univalent if it and its inverse are univalent functions together. We also discuss other concepts and important terms.