A criterion for univalent meromorphic functions

Let D = {z ∈ C, |z| < 1} and A(p) be the set of meromorphic functions in D possessing only simple pole at the point p with p ∈ (0 , 1). The aim of this paper is to give a criterion by mean of conditions on the parameters α, β ∈ C, λ > 0 and 1 ∈ A(p) for functions in the class denoted Pα,β ;h(p ; λ) of functions f ∈ A(p) satisfying a differential Inequality of the form α( z f (z) )′′ + β( z 1(z) )′′ ≤ λμ, z ∈ D to be univalent in the discD, where μ = ( 1−p 1+p ) 2 .