On some subclasses of m-fold symmetric analytic functions

We introduce and study a new class Qk. ; ;m/ of the functions f defined in the open unit disc and having the power series of the form f .z/ D z C amC1zmC1 C amC2zmC2 C : : : ; m D 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 interest- ing properties of these functions are studied.