Maclaurin Coefficient Estimates for a New General Subclasses of m-Fold Symmetric Holomorphic Bi-Univalent Functions
Abstract
The purpose of the present paper is to introduce and investigate two new general subclasses $\mathcal{M} \mathcal{A}_{\Sigma_{m}}(\delta, \lambda ; \alpha)$ and $\mathcal{M} \mathcal{A}_{\Sigma_{m}}(\delta, \lambda ; \beta)$ of $\Sigma_{m}$ consisting of holomorphic and m-fold symmetric bi-univalent functions defined in the open unit disk $U$. For functions belonging to the two classes introduced here, we derive estimates on the initial coefficients $\left|d_{m+1}\right|$ and $\left|d_{2 m+1}\right|$. We get new special cases for our results. In addition, Several related classes are also investigated and connections to earlier known outcomes are made.
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