Inspired by the recent works of Srivastava et al. (Appl Math Lett 23(10):1188–1192, 2010), Frasin and Aouf (Appl Math Lett 24(9):1569–1573, 2011), and Çağlar et al. (Filomat 27(7):1165–1171, 2013), we introduce and investigate in the present paper two new general subclasses of the class consisting of normalized analytic and bi-univalent functions in the open unit disk \({\mathbb {U}}=\{z\in {\mathbb {C}}:\left| z\right| <1\}\). For functions belonging to these general subclasses introduced here, we obtain estimates on the Taylor–Maclaurin coefficients \(|a_{2}|\) and \(|a_{3}|\). Several connections to some of the earlier known results are also pointed out. The results presented in this paper would generalize and improve those in related works of several earlier authors.

受到Srivastava等人最近工作的启发。（Appl Math Lett 23（10）：1188–1192，2010），Frasin和Aouf（Appl Math Lett 24（9）：1569–1573，2011）和Çağlar等。（Filomat 27（7）：1165–1171，2013），我们在本文中介绍并研究了两个新的通用子类，它们是开放单元盘\（{\ mathbb {U }} = \ {z \ in {\ mathbb {C}}：\ left | z \ right | <1 \} \）中。对于属于此处介绍的这些一般子类的函数，我们获得泰勒-麦克劳林系数\（| a_ {2} | \）和\（| a_ {3} | \）的估计值。还指出了一些与一些较早已知结果的联系。本文提出的结果将概括和完善几位早期作者的相关工作中的结果。