Initial Coefficient Bounds for a General Class of Bi-Univalent Functions

Recently, Srivastava et al. [22] reviewed the study of coefficient problems for bi-univalent functions. Inspired by the pioneering work of Srivastava et al. [22], there has been triggering interest to study the coefficient problems for the different subclasses of bi-univalent functions (see, for example, [1, 3, 6, 7, 27, 29],). Motivated essentially by the aforementioned works, in this paper we propose to investigate the coefficient estimates for a general class of analytic and bi-univalent functions. Also, we obtain estimates on the coefficients vertical bar a(2)vertical bar and vertical bar a(3)vertical bar for functions in this new class. Further, we discuss some interesting remarks, corollaries and applications of the results presented here.