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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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