We establish the existence of a strong convergent selection of a modified Mann-Reich-Sabach iteration scheme for approximating the common elements of the set of fixed points of a multivalued (or single-valued) strictly pseudocontractive-type mapping and the set of solutions of an equilibrium problem for a bifunction in a real Hilbert space . This work is a continuation of the study on the computability and applicability of algorithms for approximating the solutions of equilibrium problems for bifunctions involving the construction of a sequence of closed convex subsets of from an arbitrary and a sequence of the metric projections of into . The obtained result is a partial resolution of the controversy over the computability of such algorithms in the contemporary literature.
"On Computability and Applicability of Mann-Reich-Sabach-Type Algorithms for Approximating the Solutions of Equilibrium Problems in Hilbert Spaces." Abstr. Appl. Anal. 2018 1 - 9, 2018. https://doi.org/10.1155/2018/7218487