Auxiliary principle for a system of generalized set-valued nonlinear mixed variational-like inequalities in Banach spaces
type: Item
instance of: scholarly article
title: Auxiliary principle for a system of generalized set-valued nonlinear mixed variational-like inequalities in Banach spaces
zbMATH Open document ID: 1497.47087
DOI: 10.1155/2019/5353748
author: Xiaolin Zhan
author: L. C. Ceng
author: Yangqing Qiu
published in: Journal of Function Spaces
publication date: 2019-03-21T00:00:00Z
review text: Summary: In this paper, the auxiliary principle technique is extended to study a system of generalized nonlinear mixed variational-like inequalities problem for set-valued mappings without compact values in Banach spaces with \(p\)-uniformly convex bidual spaces. First, the existence of the solutions of the related auxiliary problem is proved. Then, a new iterative algorithm based on the system of auxiliary variational inequalities is constructed. Finally, both the existence of the solutions of the original problem and the convergence of the iterative sequences generated by the algorithm are proved. We also present a numerical example to demonstrate the result. Our results improve and extend some known results.
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 47H04
zbMATH DE Number: 7040452
zbMATH Keywords: generalized nonlinear mixed variational-like inequalities
zbMATH Keywords: Banach spaces
zbMATH Keywords: iterative algorithm
zbMATH Keywords: convergence
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2019/5353748
OpenAlex ID: W2907980991
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Wikidata QID: Q128644437
description: scientific article; zbMATH DE number 7040452