Duality techniques for certain integral transforms to be starlike

For β < 1, let Pγ (β) denote the class of all normalized analytic functions f such that Re{ei((1-γ)f(z)/z + γf′(z) - β)} > 0, z ∈ Δ, for some ∈ ℝ. Let S* (μ), 0 ≤ μ < 1, denote the usual class of starlike functions of order μ, S*(μ) = {f: Re(zf′(z)/f(z)) > μ, z ∈ Δ}. I[[n this paper we find conditions so that the integral transform Vλ(f)(z) = ∫01 λ(t) f(tz)/t dt carries Pγ (β) into S*(μ). We provide a number of applications for certain special choices of λ (t). These results extend previously known results by a number of authors. © 2004 Elsevier Inc. All rights reserved.