Initial coefficient bounds on some subclasses of m-fold symmetric bi-univalent functions

In this work, we consider two new subclasses of function class consisting of analytic and m-fold symmetric bi-univalent functions in the open unit disc U. Furthermore, for functions in each of the subclasses introduced in the present investigation, we obtain non-sharp bounds on the initial coefficients 1ma  and 21 ma  . Lastly, several closely-related earlier known results are indicated in the form of corollaries. This shows that, in certain cases, our estimates improve some of those existing coefficient bounds.