On some subclasses of mm-fold symmetric analytic functions

We introduce and study a new class Qk(α,β,m)Qk(α,β,m) of the functions ff defined in the open unit disc and having the power series of the form f(z)=z+am+1zm+1+am+2zm+2+…,m=1,2,…. This class generalizes the concept of bounded Mocanu variation and contains several known classes of analytic functions such as those of bounded radius rotation and alpha-starlike functions. Integral representation, the arclength problem and some other interesting properties of these functions are studied.