On Computability and Applicability of Mann-Reich-Sabach-Type Algorithms for Approximating the Solutions of Equilibrium Problems in Hilbert Spaces - F. O. Isiogugu; P. Pillay; P. U. Nwokoro (Abstract and Applied Analysis)
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 F(T) of a multivalued (or single-valued) k-strictly 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 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 Knn=1∞ of closed convex subsets of H from an arbitrary x0∈H and a sequence xnn=1∞ of the metric projections of x0 into Kn. The obtained result is a partial resolution of the controversy over the computability of such algorithms in the contemporary literature.