ABSTRACT
I f' (z) - 11 < 1 does not imply f E S *. This section describes some of the relationships between the classes t< and S *. The first part of this section deals with the problem of determining subsets D in the right-half plane such that f' (z) E D implies f E S *, and the inverse problem of determining subsets E in the right-half plane such that zf'(z)/ f(z) E E
which improves ( II smooths out II ) the properties of the original function. In
this light, one would expect that for certain integral operators we would
have I ( t<) c S *. Problems of this variety will be considered in the second part of this section.
