Duality for hadamard products applied to certain integral transforms

Let A1 be the class of functions analytic in the unit disk and normalized by f(0)= f′–1=0. We shall investigate the integral transform where λ is a non-negative real valued function normalized by From our main results we get conditions on the number β and the function λ such that V λ(f) is starlike of order γ(0 ≤ γ ≤ 1/2) when f has the property that Re[e iα (f′(z)–β)]> 0. We also find conditions implying that F=V λ(f) satisfies the starlikeness condition . As examples we study various choices of λ(t), related to classical integral transforms.