Initial Coefficient Estimates for a Certain Subclasses of $m$-Fold Symmetric Bi-Univalent Functions Involving $\phi$-Pseudo-Starlike Functions Defined by Mittag-Leffler Function

Abstract

In the present investigation, we introduce and study a certain subclasses $\mathcal{H}_{\Sigma_{m}}(\eta,\gamma,\lambda,\delta,\tau,\phi,\upsilon;\alpha)$ and $\mathcal{H}_{\Sigma_{m}}^{*}(\eta,\gamma,\lambda,\delta,\tau,\phi,\upsilon;\beta)$ of analytic and m-fold symmetric bi-univalent functions involving $\phi$-pseudo-starlike functions associated with Mittag-Leffler Function. We establish upper bounds for the second and third Taylor-Maclaurin coefficients for functions in each of these subclasses. Furthermore, we indicate several certain special cases for our results.