  The paper considers a split inverse problem involving component equilibrium
problems in Hilbert spaces. This problem therefore is called the split
equilibrium problem (SEP). It is known that almost solution methods for solving
problem (SEP) are designed from two fundamental methods as the proximal point
method and the extended extragradient method (or the two-step proximal-like
method). Unlike previous results, in this paper we introduce a new algorithm,
which is only based on the projection method, for finding solution
approximations of problem (SEP), and then establish that the resulting
algorithm is weakly convergent under mild conditions. Several of numerical
results are reported to illustrate the convergence of the proposed algorithm
and also to compare with others.
