Univalence and starlikeness of nonlinear integral transform of certain class of analytic functions

Let U(λ, μ) denote the class of all normalized analytic functions f in the unit disk |z| < 1 satisfying the condition For f ∈ U(λ, μ) with μ ≤ 1 and 0 ≠ μ1 ≤ 1, and for a positive real-valued integrable function φ defined on [0,1] satisfying the normalized condition _ 1 0 φ(t) dt = 1, we consider the transform Gφf (z) defined by In this paper, we find conditions on the range of parameters λ and μ so that the transform Gφf is univalent or star-like. In addition, for a given univalent function of certain form, we provide a method of obtaining functions in the class U(λ, μ). © Printed in India.