LetA1be the class of functions analytic in the unit disk and normalized byf(0)=f′–1=0. We shall investigate the integral transformwhere λ is a non-negative real valued function normalized byFrom our main results we get conditions on the number β and the function λ such thatVλ(f) is starlike of order γ(0 ≤ γ ≤ 1/2) whenfhas the property that Re[eiα(f′(z)–β)]> 0. We also find conditions implying thatF=Vλ(f) satisfies the starlikeness condition. As examples we study various choices of λ(t), related to classical integral transforms.