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, issue 1

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 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 {Kn} n=1∞ of closed convex subsets of H from an arbitrary x0 ∈ H and a sequence {xn} n=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.

Date: 2018
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https://doi.org/10.1155/2018/7218487

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2018:y:2018:i:1:n:7218487

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