ABSTRACT

F = ly[ f ], where ly is defined by (8.2-13). If F(z) =F-0 for z E U, then

As an example of Theorem 8.2i, consider

(1 2)1-a f(z) = + z • z

and from Theorem 8.2i we deduce that F E }:.t ( f3) , with f3 = [3( a, "() ;::: 0 given by (8.2-21). In particular, this shows that F is starlike univalent. At the end point a = -1/('Y + 1), we deduce that

For our next result on integrals of meromorphic functions we take advantage

of the fact that if f E }:.n, then 1