The univalence of an integral

Let f ( z ) f(z) be a normalized function, analytic and univalent in the open unit disc. It is shown that if g ( z ) = ∫ 0 z ( f ( t ) / t ) α d t g(z) = \int _0^z {{{(f(t)/t)}^\alpha }dt} , then g g is univalent in the open unit disc if α \alpha is a complex number satisfying 0 ≦ | α | ≦ ( √ 2 − 1 ) / 4 0 \leqq |\alpha | \leqq (\surd 2 - 1)/4 .