We establish the strong convergence of a selection of an Ishikawa-Reich-Sabach iteration scheme for approximating the common elements of the set of fixed points F(T) of a multi-valued (or single- valued) pseudocontractive-type mapping T and the set of solutions EP(F) of an equilibrium problem for a bifunction F in a real Hilbert space H. This work is a contribution to the study on the computability and applicability of algorithms for approximating the solutions of equilibrium problems for bifunctions involving the construction of the sequence {Kn}∞n=1 of closed convex subsets of H from an arbitrary x0 ∈ H and the sequence {xn}∞n=1 of the metric projections of x0 into Kn. The results obtained are contributions to the resolution of the controversy over the computability and applicability of such algorithms in the contemporary literature