Coefficient estimates for a certain subclass of analytic and bi-univalent functions

In this paper, we introduce and investigate an interesting subclass HΣh,p of analytic and bi-univalent functions in the open unit disk UU. For functions belonging to the class HΣh,p, we obtain estimates on the first two Taylor–Maclaurin coefficients |a2||a2| and |a3||a3|. The results presented in this paper would generalize and improve some recent work of Srivastava et al. [H.M. Srivastava, A.K. Mishra, P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010) 1188–1192].