  The 2-sets convex feasibility problem aims at finding a point in the
intersection of two closed convex sets $A$ and $B$ in a normed space $X$. More
generally, we can consider the problem of finding (if possible) two points in
$A$ and $B$, respectively, which minimize the distance between the sets. In the
present paper, we study some stability properties for the convex feasibility
problem: we consider two sequences of sets, each of them converging, with
respect to a suitable notion of set convergence, respectively, to $A$ and $B$.
Under appropriate assumptions on the original problem, we ensure that the
solutions of the perturbed problems converge to a solution of the original
problem. We consider both the finite-dimensional and the infinite-dimensional
case. Moreover, we provide several examples that point out the role of our
assumptions in the obtained results.
