Existence and iterative approximations of solutions for mixed quasi-variational-like inequalities in Banach spaces

被引：11

作者：

Liu, Zeqing ^{[1
]}

Chen, Zhengsheng ^{[1
]}

Kang, Shin Min ^{[2
,3
]}

Ume, Jeong Sheok ^{[4
]}

机构：

[1] Liaoning Normal Univ, Dept Math, Dalian 116029, Liaoning, Peoples R China

[2] Gyeongsang Natl Univ, Dept Math, Chinju 660701, South Korea

[3] Gyeongsang Natl Univ, Res Inst Nat Sci, Chinju 660701, South Korea

[4] Changwon Natl Univ, Dept Appl Math, Chang Won 641773, South Korea

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2008年 / 69卷 / 10期

关键词：

Mixed quasi-variational-like inequality; Iterative algorithm; KKM theorems; Auxiliary principle technique; Strongly monotone mapping; Relaxed cocoercive mapping; Cocoercive mapping; Partially relaxed monotone mapping;

D O I：

10.1016/j.na.2007.09.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce and investigate a new class of mixed quasi-variational-like inequalities in reflexive Banach spaces. By applying a minimax inequality due to Ding-Tan and a lemma due to Chang, we establish some existence and uniqueness results of solution for the mixed quasi-variational-like inequality. Next, by Ming a KKM theorem due to Fan and an auxiliary principle technique due to Cohen, we suggest two iterative algorithms and study the convergence criteria of iterative sequences generated by the iterative algorithms. Our results extend, improve and unify several known results in the literature. (C) 2007 Elsevier Ltd. All rights reserved.

引用

页码：3259 / 3272

页数：14

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