Estimates for the Initial Coefficients of Bi-univalent Functions

[[abstract]]A bi-univalent function is a univalent function defined on the unit disk for which the inverse function has a univalent extension to the unit disk. The paper of H. M. Srivastava, A. K. Mishra and P. Gochhayat [Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010), no. 10, 1188–1192] renewed the investigation of the estimate on initial coefficients of bi-univalent functions. In this paper, estimates for the initial coefficients of bi-univalent functions belonging to certain classes defined by subordination and of functions for which f and f−1 belong to different subclasses of univalent functions are derived. Improvement of the earlier known estimates were also pointed out