Sandwich-type results for a class of convex integral operators

Let H(U) be the space of analytic functions in the unit disk U. For the integral operator , with K⊂H(U), defined by , where α,β,γ,δ∈ℂ and ϕ,φ∈H(U), we will determine sufficient conditions on g1, g2, α, β and γ, such that implies . The symbol “≺” stands for subordination, and we call such a kind of result a sandwich-type theorem.In addition, is the largest function and the smallest function so that the left-hand side, respectively the right-hand side of the above implications hold, for all f functions satisfying the assumption. We give a particular case of the main result obtained for appropriate choices of functions ϕ and φ, that also generalizes classic results of the theory of differential subordination and superordination.