A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems

Motivated essentially by the recent works of Srivastava et al. [10], Frasin and Aouf [6], Xu et al. [15], and other authors, the authors of the present sequel investigate the coefficient estimate problems associated with an interesting general subclass BΣh,p(λ) of analytic and bi-univalent functions in the open unit disk UU, which is introduced here. In particular, for functions belonging to this general class BΣh,p(λ), the problems involving the estimates on the first two Taylor–Maclaurin coefficients |a2||a2| and |a3||a3| are investigated. The results presented in this paper generalize and improve the aforecited recent works of Frasin and Aouf [6] and Xu et al. [15] (see also a closely-related earlier investigation by Srivastava et al. [10]).