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2018 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
Abstr. Appl. Anal. 2018: 1-9 (2018). DOI: 10.1155/2018/7218487

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 E P ( 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 { K n } n = 1 of closed convex subsets of H from an arbitrary x 0 H and a sequence { x n } n = 1 of the metric projections of x 0 into K n . The obtained result is a partial resolution of the controversy over the computability of such algorithms in the contemporary literature.

Citation

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F. O. Isiogugu. P. Pillay. P. U. Nwokoro. "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

Information

Received: 18 November 2017; Revised: 10 May 2018; Accepted: 16 September 2018; Published: 2018
First available in Project Euclid: 16 November 2018

zbMATH: 07029293
MathSciNet: MR3864592
Digital Object Identifier: 10.1155/2018/7218487

Rights: Copyright © 2018 Hindawi

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