Abstract Considering the interesting results obtained recently by studying Rabotnov function, in this paper using the normalized Rabotnov function and the concept of subordination related with the Lucas Balancing polynomial, we defined two new subclasses of the bi-starlike and biconvex function of complex order in the open unit disc and obtained bounds of the initial Taylor-Maclaurin coefficients for functions in these classes. Furthermore, we have determined the Fekete-Szegö inequalities for function in the above mentioned classes. Several related corollaries are also presented.
Vijaya et al. (Fri,) studied this question.