Given a partial order R_≤ over a set D, the set of upper bounds under R of a subset S of D is commonly defined as { y ∈ D | ∀ x ∈ S, x R y }.

(The set of lower bounds of S may be defined as the set of upper bounds of S under the converse relation R^-1)

Is there a common name for the generalization of this notion where R is not a partial order, and is possibly a heterogenous relation between domain D and codomain D' (hence the y would be elements of the codomain)? This would be a subset of the image of S under R (and conversely, the dual notion would be a subset of the preimage).