A new hybrid projection algorithm for system of equilibrium problems and variational inequality problems and two finite families of quasi-\(\phi\)-nonexpansive mappings
type: Item
instance of: scholarly article
title: A new hybrid projection algorithm for system of equilibrium problems and variational inequality problems and two finite families of quasi-\(\phi\)-nonexpansive mappings
zbMATH Open document ID: 1263.49007
DOI: 10.1155/2013/107296
author: Pongrus Phuangphoo
author: Poom Kumam
published in: Abstract and Applied Analysis
publication date: 2013-05-08T00:00:00Z
review text: Summary: We introduce a modified Mann's iterative procedure by using the hybrid projection method for finding the common solution of a system of equilibrium problems for a finite family of bifunctions satisfying certain conditions, the common solution of fixed-point problems for two finite families of quasi-\(\phi\)-nonexpansive mappings, and the common solution of variational inequality problems for a finite family of continuous monotone mappings in a uniformly smooth and strictly convex real Banach space. Then, we prove a strong convergence theorem of the iterative procedure generated by some mild conditions. Our result presented in this paper improves and generalizes some well-known results in the literature.
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 90C33
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 6161306
zbMATH Keywords: modified Mann's iterative procedure
zbMATH Keywords: hybrid projection algorithm
zbMATH Keywords: equilibrium problems
zbMATH Keywords: variational inequalities
zbMATH Keywords: quasi-\(\phi\)-nonexpansive mappings
Wikidata QID: Q58915291
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/107296
OpenAlex ID: W2092248488
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description: scientific article; zbMATH DE number 6161306