Subordinants of differential superordinations

Let Ω be any set in the complex plane ℂ, let p be analytic in the unit disk U and let ψ (r, s, t; z). In this article we consider the problem of determining properties of functions p that satisfy the differential superordination Ω ⊂ {ψ(p(z), z 2 p"(z);z)|z ∈ U}.