Given a partial order $R_{\leq}$ over a set $D$, the set of upper bounds under $R$ of a subset $S$ of $D$ is commonly defined as $\{ y \in D | \ \forall x\in S, x R y \}$.

(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).