Hybrid viscosity approaches to general systems of variational inequalities with hierarchical fixed point problem constraints in Banach spaces
type: Item
instance of: scholarly article
title: Hybrid viscosity approaches to general systems of variational inequalities with hierarchical fixed point problem constraints in Banach spaces
zbMATH Open document ID: 1474.49019
DOI: 10.1155/2014/945985
author: L. C. Ceng
author: A. Latif
author: Saleh A. Al-Mezel
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: The purpose of this paper is to introduce and analyze hybrid viscosity methods for a general system of variational inequalities (GSVI) with hierarchical fixed point problem constraint in the setting of real uniformly convex and 2-uniformly smooth Banach spaces. Here, the hybrid viscosity methods are based on Korpelevich's extragradient method, viscosity approximation method, and hybrid steepest-descent method. We propose and consider hybrid implicit and explicit viscosity iterative algorithms for solving the GSVI with hierarchical fixed point problem constraint not only for a nonexpansive mapping but also for a countable family of nonexpansive mappings in \(X\), respectively. We derive some strong convergence theorems under appropriate conditions. Our results extend, improve, supplement, and develop the recent results announced by many authors.
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 7023368
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/945985
OpenAlex ID: W2066522114
Wikidata QID: Q59043026
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description: scientific article; zbMATH DE number 7023368