  We extend the concept of well-posedness to the split equilibrium problem and
establish Furi-Vignoli-type characterizations for the well-posedness. We prove
that the well-posedness of the split equilibrium problem is equivalent to the
existence and uniqueness of its solution under certain assumptions on the
bifunctions involved. We also characterize the generalized well-posedness of
the split equilibrium problem via the Kuratowski measure of noncompactness. We
illustrate our theoretical results by several examples.
