THEOREM 8.2j. [ 247 ] Let a < 1, 0 < y, f and
Sanford S. Miller, Petru T. Mocanu · 2000
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/(&s;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