  The notion of well-posedness has drawn the attention of many researchers in
the field of nonlinear analysis, as it allows to explore problems in which
exact solutions are not known and/or computationally hard to compute. Roughly
speaking, for a given problem, well-posedness guarantees the convergence of
approximations to exact solutions via an iterative method. Thus, in this paper
we extend the concept of Levitin-Polyak well-posedness to split equilibrium
problems in real Banach spaces. In particular, we establish a metric
characterization of Levitin-Polyak well-posedness by perturbations and also
show an equivalence between Levitin-Polyak well-posedness by perturbations for
split equilibrium problems and the existence and uniqueness of their solutions.
