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 and P. U. Nwokoro

Abstract and Applied Analysis, 2018, vol. 2018, 1-9

Abstract:

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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:7218487

DOI: 10.1155/2018/7218487

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