On computability and applicability of Mann-Reich-Sabach-type algorithms for approximating the solutions of equilibrium problems in Hilbert spaces
type: Item
instance of: scholarly article
title: On computability and applicability of Mann-Reich-Sabach-type algorithms for approximating the solutions of equilibrium problems in Hilbert spaces
zbMATH Open document ID: 1470.47061
DOI: 10.1155/2018/7218487
published in: Abstract and Applied Analysis
publication date: 2019-02-25T00:00:00Z
review text: Summary: 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 \(\{K_n \}_{n = 1}^{\infty}\) of closed convex subsets of \(H\) from an arbitrary \(x_0 \in H\) and a sequence \(\{x_n \}_{n = 1}^{\infty}\) 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.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 7029293
zbMATH Keywords: strong convergence
zbMATH Keywords: modified Mann-Reich-Sabach iteration scheme
zbMATH Keywords: fixed points
zbMATH Keywords: \(k \)-strictly pseudocontractive-type mappings
zbMATH Keywords: equilibrium problem
zbMATH Keywords: bifunctions
zbMATH Keywords: real Hilbert spaces
author: Felicia Obiageli Isiogugu
author: Paranjothi Pillay
author: Peter Uche Nwokoro
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/7218487
OpenAlex ID: W2895647793
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Wikidata QID: Q129178924
description: scientific article; zbMATH DE number 7029293