Hybrid and relaxed Mann iterations for general systems of variational inequalities and nonexpansive mappings
type: Item
instance of: scholarly article
title: Hybrid and relaxed Mann iterations for general systems of variational inequalities and nonexpansive mappings
zbMATH Open document ID: 1364.47011
DOI: 10.1155/2013/102820
author: A. E. Al-Mazrooei
author: A. A. N. Abdou
author: A. Latif
author: L. C. Ceng
published in: Abstract and Applied Analysis
publication date: 2014-06-20T00:00:00Z
review text: Summary: We introduce hybrid and relaxed Mann iteration methods for a general system of variational inequalities with solutions being also common solutions of a countable family of variational inequalities and common fixed points of a countable family of nonexpansive mappings in real smooth and uniformly convex Banach spaces. Here, the hybrid and relaxed Mann iteration methods are based on Korpelevich's extragradient method, viscosity approximation method, and Mann iteration method. Under suitable assumptions, we derive some strong convergence theorems for hybrid and relaxed Mann iteration algorithms not only in the setting of uniformly convex and 2-uniformly smooth Banach space but also in a uniformly convex Banach space having a uniformly Gâteaux differentiable norm. The results presented in this paper improve, extend, supplement, and develop the corresponding results announced in the earlier and very recent literature.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 6306023
zbMATH Keywords: hybrid relaxed iteration methods
zbMATH Keywords: strong convergence
zbMATH Keywords: uniformly convex Banach space
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/102820
OpenAlex ID: W2011239293
Wikidata QID: Q58915281
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description: scientific article; zbMATH DE number 6306023