Coefficient Estimates for the Generalized Subclass of Analytic and Bi-univalent Functions

Abstract

In this paper, we introduce and investigate an interesting subclass $\mathcal{B}_\Sigma^{h,p}(\lambda)$ of analytic and bi-univalent functions in the open unit disk $\mathbb{U}$. For functions belonging to the class $\mathcal{B}_\Sigma^{h,p}(\lambda)$, obtain estimates on the first two coefficients $|a_2|$ and $|a_3|$. The results presented in this paper generalize and improve some recent works of Frasin et al. [B.A.Frasin, M.K.Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett. 24(2011) 1569-1573] and Srivastava et al. [Qing-Hua Xu, Ying-Chun Gui, H.M.Srivastava, coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett. Appl. Math. Lett. 25: 990-994, 2012].