Upper Bounds for Certain Families of m-Fold Symmetric Bi-Univalent Functions Associating Bazilevic Functions with λ-Pseudo Functions

Abstract

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