A class of superordination-preserving integral operators

Abstract Let H(U) be the space of all analytic functions in the unit disk U. For the integral operator Aβ,γ: K → H(U), with K ⊂ H(U), defined by where β, γ ϵ C , we will determine sufficient conditions on g, β and γ such that the next implication holds: In addition, we will prove that is the largest function so that the right-hand side of the above implication holds, for all f functions satisfying the left-hand side differential super-ordination. The concept of differential superordination was introduced by S.S. Miller and P.T. Mocanu in [7] like a dual problem of differential subordination [6].