Coefficient Bounds for a New Families of m-Fold Symmetric Bi-Univalent Functions Defined by Bazilevic Convex Functions

Abstract

In this paper, we find upper bounds for the first two Taylor-Maclaurin $\left|a_{m+1}\right|$ and $\left|a_{2m+1}\right|$ for two new families $L_{\Sigma_m}(\delta, \gamma ; \alpha)$ and $L_{\Sigma_m}^{*}(\delta, \gamma ; \alpha)$ of holomorphic and $m$-fold symmetric bi-univalent functions associated with the Bazilevic convex functions defined in the open unit disk $U$. Further, we point out several certain special cases for our results.

Two Families of m-fold Symmetric Bi-univalent Functions Involving a Linear Combination of Bazilevic Starlike and Convex Functions

“…Recently, many authors investigated bounds for various subfamilies of -fold biunivalent functions (see [1,4,7,13,17,19,20,23,25,26,29,31,32]).…”