Existence and iterative approximations of solutions for mixed quasi-variational-like inequalities in Banach spaces
type: Item
instance of: scholarly article
title: Existence and iterative approximations of solutions for mixed quasi-variational-like inequalities in Banach spaces
zbMATH Open document ID: 1182.47048
author: Zhengsheng Chen
author: Zeqing Liu
author: Shin Min Kang
author: Jeong Sheok Ume
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2008-11-20T00:00:00Z
review text: In this paper, a new class of mixed quasi-variational-like inequalities in reflexive Banach space is introduced and investigated. Some existence and uniqueness results for solutions of the mixed quasi-variational-like inequalities are established by applying a minimax inequality due to Ding-Tan and a lemma due to Chang. Two iterative algorithms and the convergence criteria of iterative sequences are studied by using a KKM theorem due to Fan and an auxiliary principle technique due to Cohen. The results extend, improve and unify several known results in the literature.
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 5369414
zbMATH Keywords: mixed quasi-variational-like inequality
zbMATH Keywords: iterative algorithm
zbMATH Keywords: KKM theorem
zbMATH Keywords: auxiliary principle technique
zbMATH Keywords: strongly monotone mapping
zbMATH Keywords: relaxed cocoercive mapping
zbMATH Keywords: cocoercive mapping
zbMATH Keywords: partially relaxed monotone mapping
reviewed by: Zhang Xian
MaRDI profile type: Publication
full work available at URL: j.na.2007.09.015
OpenAlex ID: W2081383669
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DOI: 10.1016/J.NA.2007.09.015
description: scientific article; zbMATH DE number 5369414