Coefficient estimates for special subclasses of k-fold symmetric bi-univalent functions

Abstract

In the present paper, we consider two new subclasses Nk (μ,) and Nk (μ,) of k consisting of analytic and k-fold symmetric bi-univalent functions defined in the open unit disc U = {z : z 2 C and |z| < 1}. For functions belonging to the two classes introduced here, we derive their normalized forms. Furthermore, we find estimates of the initial coefficients |ak+1| and |a2k+1| for these functions. Several related classes are also considered and connections to previously known results are made.