Analytic functions with bounded Mocanu variation generalize the concept of α-convexity in the unit disc. We introduce and
study certain classes of such functions. Inclusion results are obtained and a sharp radius problem is solved.
In the paper we prove that the complex analytic functions are (ordinarily) density continuous. This stays in contrast with the fact that even such a simple function asG:R2?R2,G(x,y)=(x,y3), is not density continuous . We will also characterize those analytic functions which are strongly density continuous at the given pointa ? C. From this we conclude that a complex analytic functionf is strongly density continuous if and only iff(z)=a+bz, wherea, b ? C andb is either real or imaginary.