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

Abstract

In this work, we introduce and investigate a subclass
$\mathcal{H}_{\Sigma_{m}}^{h, p}(\tau,\gamma)$ of
analytic and bi-univalent functions when both
$f(z)$ and $f^{-1}(z)$ are $m$-fold symmetric
in the open unit disk $\mathbb{U}$.
Moreover, we find upper bounds for the initial coefficients
$|a_{m + 1}|$ and $|a_{2m + 1}|$ for functions belonging
to this subclass $\mathcal{H}_{\Sigma_{m}}^{h, p}(\tau,\gamma)$.
The results presented in this paper would generalize and improve those
that were given in several recent works.