Certain classes of bi-univalent functions with bounded boundary variation

In their pioneering work dated 2010 on the subject of bi-univalent functions, Srivastava et al. actually revived the study of the coefficient problems involving bi-univalent functions in recent years. Inspired by the pioneering work of Srivastava et Hi., there has been triggering interest to study the coefficient problems for many different subclasses of bi univalent functions. Motivated largely by a number of sequels to the investigation by Srivastava et al., in this paper, we consider certain classes of bi-univalent functions to obtain the estimates of their second and third Taylor-Maclaurin coefficients. Further, certain special cases are also indicated. Some interesting remarks about the results presented here are also discussed.