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

共 50 条

[41] Existence of Solutions for New Systems of Generalized Mixed Vector Variational-like Inequalities in Reflexive Banach Spaces
Plubtieng, Somyot
Sriprad, Wanna
THAI JOURNAL OF MATHEMATICS, 2011, 9 (01): : 219 - 235
[42] General iterative algorithms for solving mixed quasi-variational-like inclusions
Zeng, Lu-Chuan
Ansari, Qamrul Hasan
Yao, Jen-Chih
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (10) : 2455 - 2467
[43] Existence of solutions for generalized nonlinear vector quasi-variational-like inequalities with set-valued mappings
Husain, Shamshad
Gupta, Sanjeev
FILOMAT, 2012, 26 (05) : 909 - 916
[44] Generalized quasi-variational-like hemivariational inequalities
Xiao, Yi-bin
Huang, Nan-jing
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 69 (02) : 637 - 646
[45] Generalized vector quasi-variational-like inequalities
Peng, Jian-Wen
Yang, Xin-Min
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2006, 2006 (1) : 1 - 11
[46] Existence of solutions of generalized variational inequalities in reflexive Banach spaces
Wong, Mu-Ming
Ansari, Qamrul Hasan
Yao, Jen-Chih
APPLIED MATHEMATICS LETTERS, 2009, 22 (02) : 197 - 201
[47] Generalized vector quasi-variational-like inequalities
Jian-Wen Peng
Xin-Min Yang
Journal of Inequalities and Applications, 2006
[48] Generalized vector quasi-variational-like inequalities
Peng, Jian-wen
MATHEMATICAL INEQUALITIES & APPLICATIONS, 2007, 10 (02): : 417 - 426
[49] The generalized vector quasi-variational-like inequalities
Ding, XP
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1999, 37 (06) : 57 - 67
[50] SOME REMARKS ON VARIATIONAL-LIKE AND QUASI-VARIATIONAL-LIKE INEQUALITIES
DIEN, NH
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1992, 46 (02) : 335 - 342

← 1 2 3 4 5 →