On Some Subclasses of m-fold Symmetric Bi-univalent Functions associated with the Sakaguchi Type Functions
Abstract
In the present investigation, we introduce the subclasses $\Lambda_{\Sigma_m}^{\rightthreetimes}(\sigma,\phi,\upsilon)$ and $\Lambda_{\Sigma_m}^{\rightthreetimes}(\sigma,\gamma,\upsilon)$ of $m$-fold symmetric bi-univalent function class $\Sigma_m$, which are associated with the Sakaguchi type of functions and defined in the open unit disk. Further, we obtain estimates on the initial coefficients $b_{m+1}$ and $b_{2m+1}$ for the functions of these subclasses and find out connections with some of the familiar classes.
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