Generalized nonlinear variational-like inequalities in reflexive Banach spaces

被引：10
|
作者：
Liu, Z [1 ]
Ume, JS
Kang, SM
机构：
[1] Liaoning Normal Univ, Dept Math, Dalian, Liaoning, Peoples R China
[2] Changwon Natl Univ, Dept Appl Math, Chang Won, South Korea
[3] Gyeongsang Natl Univ, Dept Math, Chinju, South Korea
[4] Gyeongsang Natl Univ, Res Inst Nat Sci, Chinju, South Korea
来源：
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2005年 / 126卷 / 01期
关键词：
minimax inequalities; auxiliary principle technique; generalized nonlinear variational-like inequalities; fixed points; existence; algorithms; convergence; reflexive Banach spaces;
D O I：
10.1007/s10957-005-2666-1
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
In this paper, we introduce and study a new class of generalized nonlinear variational-like inequalities in reflexive Banach spaces. By applying the auxiliary principle technique due to Glowinski-Lions-Tremolieres (Ref. 1) and the minimax inequality due to Ding-Tan (Ref. 2), we establish existence and uniqueness theorems for solutions of generalized nonlinear variational-like inequalities; also, we suggest two general algorithms and prove the convergence of the iterative sequences generated by the algorithms. Our results extend, improve, and unify several known results due to Cohen, Ding, Bose, Parida-Sahoo-Kumar, Dien, Ding-Tarafdar, Noor, and others.
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页码：157 / 174
页数：18
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