Coefficient estimates for a new general subclass of analytic bi-univalent functions

Abstract

In a very recent paper, Yousef et al. [Anal. Math. Phys. 11: 58 (2021)] introduced two new subclasses of analytic and bi-univalent functions and obtained the estimates on the first two Taylor-Maclaurin coefficients $\left\vert a_{2}\right\vert $ and $\left\vert a_{3}\right\vert $ for functions belonging to these classes. In this study, we introduce a general subclass $\mathcal{B}_{\Sigma }^{h,p}\left( \lambda ,\mu ,\delta \right) $ of analytic and bi-univalent functions in the unit disk $\mathbb{U}$, and investigate the coefficient bounds for functions belonging to this general function class. Our results improve the results of the above mentioned paper of Yousef et al.