On some subclasses of m-fold symmetric analytic functions
We introduce and study a new class Q(k)(alpha, beta, m) of the functions f defined in the open unit disc and having the power series of the form f(z) = z + a(m+1)z(m+1) + a(m+2)z(m+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. (C) 2010 Elsevier Ltd. All rights reserved.
m-fold symmetric bounded radius rotation radius integral representation arclength problem univalent starlike