On certain analytic functions with bounded radius rotation

Certain classes Rk(μ,α);k≥2,μ>−1,0≤α<1 of analytic functions are defined in the unit disc using convolution technique. It is shown that functions in Rk(μ,α)Rk(μ,α) are of bounded radius rotation. It is proved that Rk(μ,α)Rk(μ,α) and some other newly introduced related classes are invariant under the generalized Bernardi integral operator. The converse case as a radius problem is also considered. Theorems proved in this paper are best possible in some sense.